Graphs - SAT Math

Positive correlation. Upward trend indicates both variables increase together.

Line of best fit (or trend line). Drawn through data points to show the overall pattern or trend.

Positive correlation. Positive slope means both variables increase together.

A weak relationship between the variables. Small changes in y correspond to changes in x.

Positive correlation. As one variable increases, the other also increases.

A relationship involving two variables. Scatter plots specifically examine two-variable relationships.

Points trend downwards from left to right. As x increases, y decreases, showing an inverse relationship.

Points are scattered randomly with no clear trend. No predictable pattern exists between the two variables.

Groups of data points clustered together. Shows distinct groups or categories within the data set.

The rate of change between the variables. Slope shows how much y changes per unit increase in x.

The model is appropriate for the data. Random residuals suggest the linear model is valid.

The vertical axis representing the dependent variable. Also called the dependent variable because it responds to changes in x.

A point that lies far from the general pattern of the data. Look for points that don't follow the main cluster or trend.

By minimizing the distances from all points to the line. Uses least squares method to minimize total squared distances.

Predicting values outside the range of the data. Extends the trend line beyond the given data points.

Extrapolation. Predicting outside the data range carries more uncertainty.

To quantify the strength and direction of a relationship. Measures how closely the data follows a linear pattern.

Perfect positive linear relationship. All points lie exactly on an upward-sloping line.

No correlation. Random scatter with no clear pattern means variables are unrelated.

Linear relationship. Points can be approximated by a straight line.

A strong relationship between the variables. Large changes in y correspond to small changes in x.

From -1 to 1. Values closer to $\pm 1$ indicate stronger linear relationships.

No correlation. The variables are not related in a predictable way.

Negative correlation. Downward slope indicates variables move in opposite directions.

A graph that shows the relationship between two variables using points. Each point plots one x-value against one y-value to visualize patterns.

Negative correlation. Negative slope means variables move in opposite directions.

Predicting values within the range of the data. Uses the trend line between existing data points.

Independent variable. The x-axis variable is controlled or chosen first.

To display the relationship between two quantitative variables. Shows how two numerical variables relate or change together.

No linear relationship. Variables are not linearly related to each other.

No correlation. Random scatter indicates no predictable relationship between variables.

The difference between observed and predicted values. Measures how far each point deviates from the trend line.

Data points that deviate significantly from the pattern. These unusual points don't follow the overall trend.

Strong positive correlation. $0.85$ is close to $1$, indicating a strong positive relationship.

No correlation. Zero slope means y doesn't change as x changes.

Weak negative correlation. $-0.2$ is close to $0$, indicating a weak relationship.

No correlation. Zero means no linear relationship exists between the variables.

The residuals on the y-axis versus the independent variable. Helps assess whether the linear model fits the data well.

As one variable increases, the other variable also increases. Both variables move in the same direction together.

Linear regression. Method that creates the best-fitting line through data points.

Outliers are data points that deviate significantly from the trend. They can affect trend lines and correlation strength significantly.

A straight line that best represents the data on a scatter plot. Also called a trend line, it summarizes the data's relationship.

The horizontal axis representing the independent variable. Also called the independent variable because it's controlled or measured first.

To show the general direction or pattern of the data. Helps visualize the overall relationship and make predictions.

A pair of values for the two variables being compared. One coordinate from each variable creates a single data point.

To visualize the relationship between two quantitative variables. Shows how one variable changes as another changes.

Dependent variable. The y-axis variable responds to changes in the x-variable.

Correlation coefficient. The $r$ value measures strength and direction of correlation.

Correct: indicate strong correlation. Tightly clustered points show strong, not weak correlation.

Points trend upwards from left to right. As x increases, y also increases, showing a positive relationship.

$(2, -3)$. Vertex form shows $(h, k)$ as the turning point.

Solve $Ax + By = C$ for $y$. Isolate $y$ by dividing by coefficient of $y$.

$y = mx + b$. Standard form where $m$ is slope and $b$ is y-intercept.

$y = a(x - h)^2 + k$. Shows vertex $(h, k)$ and vertical shift $k$.

The rate of change or steepness of the line. Measures how much $y$ changes per unit increase in $x$.

$x = -\frac{b}{2a}$. Vertical line through the vertex of the parabola.

$(2, 0)$. Set $y = 0$ and solve for $x$.

$(x - h)^2 + (y - k)^2 = r^2$. Standard circle equation with center $(h, k)$ and radius $r$.

$x^2 + y^2 + Dx + Ey + F = 0$. Expanded form of circle equation.

(3, 2). Vertex form $(x - h)^2 + k$ has vertex at $(h, k)$.

$\frac{1}{3}$. Coefficient of $(x - 3)$ in point-slope form.

$y = 3x + 1$. Same slope, substitute point to find $b$.

-4. Parallel lines have identical slopes.

$y = 4x$. Negative reciprocal slope through given point.

Downward. Negative coefficient of $x^2$ opens downward.

$ax^2 + bx + c = 0$. Standard form with highest power of 2.

1. The constant term when $x = 0$.

$\frac{3}{4}$. Rearrange to $y = \frac{3}{4}x - 3$ to identify slope.

$-\frac{1}{2}$. Negative reciprocal of the original slope.

Point-slope form. Uses a known point $(x_1, y_1)$ and slope $m$.

$x = a$. All points have the same $x$-coordinate.

1. Set $y = 0$ and solve: $0 = 2x - 8$, so $x = 4$.

(1, 5). Substituting: $y = 2(1) + 3 = 5$, so point $(1, 5)$ satisfies the equation.

$\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. Average of the coordinates of the endpoints.

$m = \frac{y_2 - y_1}{x_2 - x_1}$. Change in $y$ over change in $x$ between two points.

$Ax + By = C$. Linear equation with integer coefficients $A$, $B$, and $C$.

$\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Pythagorean theorem applied to coordinate plane differences.

$y = b$. All points have the same $y$-coordinate.

$(3, 4)$. Average the x-coordinates and y-coordinates: $\frac{1+5}{2}, \frac{2+6}{2}$.

$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Pythagorean theorem applied to coordinate plane.

$(3, -4)$. Values of $(h, k)$ from standard form.

$y = mx + b$. Shows slope $m$ and $y$-intercept $b$ directly.

$y = mx + b$. Standard form where $m$ is slope and $b$ is y-intercept.

$y = ax^2 + bx + c$. Quadratic with degree 2 polynomial.

$Ax + By = C$. Linear equation with integer coefficients and no fractions.

1. Rearrange to $y = mx + b$ form first.

x-intercepts: $3, -2$. Set $y = 0$ to find where parabola crosses $x$-axis.

$(x - h)^2 + (y - k)^2 = r^2$. Distance from center to any point on circle equals radius.

$(0, 2)$. Set $x = 0$ and solve for $y$.

Vertical. Constant $x$-value creates vertical line.

$(x - h)^2 + (y - k)^2 = r^2$. Distance from center to any point on circle.

1. Horizontal line has zero rise over run.

Each input has exactly one output. Vertical line test ensures unique outputs.

$4$. Square root of the constant term.

Right 1 unit, up 2 units. Vertex form shows horizontal and vertical shifts.

1. Solve for $x$ when $y = 0$.

x-intercept: 6, y-intercept: -3. Set each variable to zero alternately.

Parabola. Quadratic function creates U-shaped curve.

1. Square root of the constant gives radius.

1. Set $x = 0$: $5y = 20$, so $y = 4$.

-5. Coefficient of $x$ in slope-intercept form.

$(1, 3)$. Solve the system by setting equations equal.

$(-2, -5)$. Vertex form identifies $(h, k)$ directly.

Interpolation. Predicting between existing points is generally more reliable.

Negative correlation. As one variable increases, the other decreases.

Negative correlation. Downward trend indicates one variable decreases as the other increases.

Perfect negative linear relationship. All points lie exactly on a downward-sloping line.

$(3, 4)$. Average the x-coordinates and y-coordinates: $\frac{1+5}{2}, \frac{2+6}{2}$.

Point-slope form. Uses a known point $(x_1, y_1)$ and slope $m$.

1. Set $y = 0$ and solve: $0 = 2x - 8$, so $x = 4$.

Correlation coefficient. The $r$ value measures strength and direction of correlation.

Linear regression. Method that creates the best-fitting line through data points.

To visualize the relationship between two quantitative variables. Shows how one variable changes as another changes.

Correct: indicate strong correlation. Tightly clustered points show strong, not weak correlation.

1. Set $x = 0$: $5y = 20$, so $y = 4$.

No correlation. The variables are not related in a predictable way.

Linear relationship. Points can be approximated by a straight line.

$y = mx + b$. Standard form where $m$ is slope and $b$ is y-intercept.

$\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Pythagorean theorem applied to coordinate plane differences.

Parabola. Quadratic function creates U-shaped curve.

$\frac{3}{4}$. Rearrange to $y = \frac{3}{4}x - 3$ to identify slope.

$(x - h)^2 + (y - k)^2 = r^2$. Distance from center to any point on circle.

A graph that shows the relationship between two variables using points. Each point plots one x-value against one y-value to visualize patterns.

$y = mx + b$. Shows slope $m$ and $y$-intercept $b$ directly.

Points are scattered randomly with no clear trend. No predictable pattern exists between the two variables.

Points trend downwards from left to right. As x increases, y decreases, showing an inverse relationship.

Outliers are data points that deviate significantly from the trend. They can affect trend lines and correlation strength significantly.

A pair of values for the two variables being compared. One coordinate from each variable creates a single data point.

Points trend upwards from left to right. As x increases, y also increases, showing a positive relationship.

Positive correlation. Upward trend indicates both variables increase together.

Negative correlation. Downward trend indicates one variable decreases as the other increases.

A straight line that best represents the data on a scatter plot. Also called a trend line, it summarizes the data's relationship.

By minimizing the distances from all points to the line. Uses least squares method to minimize total squared distances.

A strong relationship between the variables. Large changes in y correspond to small changes in x.

A weak relationship between the variables. Small changes in y correspond to changes in x.

No correlation. Zero slope means y doesn't change as x changes.

Predicting values within the range of the data. Uses the trend line between existing data points.

Extrapolation. Predicting outside the data range carries more uncertainty.

To quantify the strength and direction of a relationship. Measures how closely the data follows a linear pattern.

Perfect positive linear relationship. All points lie exactly on an upward-sloping line.

Strong positive correlation. $0.85$ is close to $1$, indicating a strong positive relationship.

Weak negative correlation. $-0.2$ is close to $0$, indicating a weak relationship.

The residuals on the y-axis versus the independent variable. Helps assess whether the linear model fits the data well.

The model is appropriate for the data. Random residuals suggest the linear model is valid.

Independent variable. The x-axis variable is controlled or chosen first.

The horizontal axis representing the independent variable. Also called the independent variable because it's controlled or measured first.

To show the general direction or pattern of the data. Helps visualize the overall relationship and make predictions.

No correlation. Random scatter indicates no predictable relationship between variables.

A point that lies far from the general pattern of the data. Look for points that don't follow the main cluster or trend.

Positive correlation. Positive slope means both variables increase together.

Predicting values outside the range of the data. Extends the trend line beyond the given data points.

Interpolation. Predicting between existing points is generally more reliable.

Perfect negative linear relationship. All points lie exactly on a downward-sloping line.

No correlation. Zero means no linear relationship exists between the variables.

The difference between observed and predicted values. Measures how far each point deviates from the trend line.

The vertical axis representing the dependent variable. Also called the dependent variable because it responds to changes in x.

The rate of change between the variables. Slope shows how much y changes per unit increase in x.

No linear relationship. Variables are not linearly related to each other.

Negative correlation. Negative slope means variables move in opposite directions.

From -1 to 1. Values closer to $\pm 1$ indicate stronger linear relationships.

A relationship involving two variables. Scatter plots specifically examine two-variable relationships.

Groups of data points clustered together. Shows distinct groups or categories within the data set.

Dependent variable. The y-axis variable responds to changes in the x-variable.

$(0, 2)$. Set $x = 0$ and solve for $y$.

1. The constant term when $x = 0$.

Solve $Ax + By = C$ for $y$. Isolate $y$ by dividing by coefficient of $y$.

Downward. Negative coefficient of $x^2$ opens downward.

$x = a$. All points have the same $x$-coordinate.

$(2, 0)$. Set $y = 0$ and solve for $x$.

$x = -\frac{b}{2a}$. Vertical line through the vertex of the parabola.

$(3, -4)$. Values of $(h, k)$ from standard form.

$y = b$. All points have the same $y$-coordinate.

$\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. Average of the coordinates of the endpoints.

The rate of change or steepness of the line. Measures how much $y$ changes per unit increase in $x$.

-5. Coefficient of $x$ in slope-intercept form.

$y = 3x + 1$. Same slope, substitute point to find $b$.

$Ax + By = C$. Linear equation with integer coefficients and no fractions.

$(-2, -5)$. Vertex form identifies $(h, k)$ directly.

Right 1 unit, up 2 units. Vertex form shows horizontal and vertical shifts.

$m = \frac{y_2 - y_1}{x_2 - x_1}$. Change in $y$ over change in $x$ between two points.

$x^2 + y^2 + Dx + Ey + F = 0$. Expanded form of circle equation.

x-intercept: 6, y-intercept: -3. Set each variable to zero alternately.

Each input has exactly one output. Vertical line test ensures unique outputs.

$(1, 3)$. Solve the system by setting equations equal.

x-intercepts: $3, -2$. Set $y = 0$ to find where parabola crosses $x$-axis.

$y = 4x$. Negative reciprocal slope through given point.

$\frac{1}{3}$. Coefficient of $(x - 3)$ in point-slope form.

$y = ax^2 + bx + c$. Quadratic with degree 2 polynomial.

$7$. Square root of the constant gives radius.

Vertical. Constant $x$-value creates vertical line.

1. Horizontal line has zero rise over run.

1. Rearrange to $y = mx + b$ form first.

1. Square root of the constant term.

-4. Parallel lines have identical slopes.

$-\frac{1}{2}$. Negative reciprocal of the original slope.