Creating and Graphing Two Variable Equations - Algebra
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Find the missing value: If $(2,y)$ is on $y=3x-4$, what is $y$?
Find the missing value: If $(2,y)$ is on $y=3x-4$, what is $y$?
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$y=2$. Substitute $x=2$: $y=3(2)-4=2$.
$y=2$. Substitute $x=2$: $y=3(2)-4=2$.
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Identify the equation for Fahrenheit $F$ in terms of Celsius $C$ using a linear conversion.
Identify the equation for Fahrenheit $F$ in terms of Celsius $C$ using a linear conversion.
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$F=\frac{9}{5}C+32$. Linear conversion from Celsius to Fahrenheit.
$F=\frac{9}{5}C+32$. Linear conversion from Celsius to Fahrenheit.
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What is the equation for a line with slope $4$ and $y$-intercept $-3$?
What is the equation for a line with slope $4$ and $y$-intercept $-3$?
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$y=4x-3$. Substitute slope and $y$-intercept into $y=mx+b$.
$y=4x-3$. Substitute slope and $y$-intercept into $y=mx+b$.
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What is the equation for a line with slope $-2$ and $y$-intercept $5$?
What is the equation for a line with slope $-2$ and $y$-intercept $5$?
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$y=-2x+5$. Substitute slope and $y$-intercept into $y=mx+b$.
$y=-2x+5$. Substitute slope and $y$-intercept into $y=mx+b$.
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What is the slope of the line through $(0,2)$ and $(3,11)$?
What is the slope of the line through $(0,2)$ and $(3,11)$?
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$m=3$. Use slope formula: $m=\frac{11-2}{3-0}=3$.
$m=3$. Use slope formula: $m=\frac{11-2}{3-0}=3$.
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What does the variable $x$ typically represent on a coordinate plane when graphing an equation?
What does the variable $x$ typically represent on a coordinate plane when graphing an equation?
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$x$ represents the independent variable (horizontal axis). It's the input value that can be chosen freely.
$x$ represents the independent variable (horizontal axis). It's the input value that can be chosen freely.
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What does the variable $y$ typically represent on a coordinate plane when graphing an equation?
What does the variable $y$ typically represent on a coordinate plane when graphing an equation?
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$y$ represents the dependent variable (vertical axis). It depends on the $x$-value chosen.
$y$ represents the dependent variable (vertical axis). It depends on the $x$-value chosen.
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What is the slope-intercept form of a linear equation in two variables?
What is the slope-intercept form of a linear equation in two variables?
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$y=mx+b$. Standard form with slope $m$ and $y$-intercept $b$.
$y=mx+b$. Standard form with slope $m$ and $y$-intercept $b$.
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What is the standard form of a linear equation in two variables used in Algebra $1$?
What is the standard form of a linear equation in two variables used in Algebra $1$?
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$Ax+By=C$. General linear form with integer coefficients.
$Ax+By=C$. General linear form with integer coefficients.
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What is the slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$?
What is the slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$?
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$m=\frac{y_2-y_1}{x_2-x_1}$. Change in $y$ divided by change in $x$.
$m=\frac{y_2-y_1}{x_2-x_1}$. Change in $y$ divided by change in $x$.
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What is the $y$-intercept of a line written in the form $y=mx+b$?
What is the $y$-intercept of a line written in the form $y=mx+b$?
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The $y$-intercept is $b$. The constant term gives the $y$-intercept.
The $y$-intercept is $b$. The constant term gives the $y$-intercept.
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What is the $x$-intercept of a graph, stated as a condition on $y$?
What is the $x$-intercept of a graph, stated as a condition on $y$?
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The $x$-intercept occurs where $y=0$. Set $y=0$ and solve for $x$.
The $x$-intercept occurs where $y=0$. Set $y=0$ and solve for $x$.
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What is the $y$-intercept of a graph, stated as a condition on $x$?
What is the $y$-intercept of a graph, stated as a condition on $x$?
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The $y$-intercept occurs where $x=0$. Set $x=0$ and solve for $y$.
The $y$-intercept occurs where $x=0$. Set $x=0$ and solve for $y$.
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What is the equation of a vertical line passing through $x=3$?
What is the equation of a vertical line passing through $x=3$?
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$x=3$. Vertical lines have constant $x$-coordinate.
$x=3$. Vertical lines have constant $x$-coordinate.
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What is the equation of a horizontal line passing through $y=-2$?
What is the equation of a horizontal line passing through $y=-2$?
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$y=-2$. Horizontal lines have constant $y$-coordinate.
$y=-2$. Horizontal lines have constant $y$-coordinate.
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What does it mean for an ordered pair $(x,y)$ to be a solution of an equation in two variables?
What does it mean for an ordered pair $(x,y)$ to be a solution of an equation in two variables?
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$(x,y)$ makes the equation true when substituted. The coordinates satisfy the equation exactly.
$(x,y)$ makes the equation true when substituted. The coordinates satisfy the equation exactly.
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What is the meaning of the slope $m$ in $y=mx+b$ as a rate of change?
What is the meaning of the slope $m$ in $y=mx+b$ as a rate of change?
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$m$ is the change in $y$ per $1$ unit change in $x$. Slope measures the rate of change.
$m$ is the change in $y$ per $1$ unit change in $x$. Slope measures the rate of change.
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What is the first step to graph an equation in two variables by making a table?
What is the first step to graph an equation in two variables by making a table?
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Choose $x$-values and compute the corresponding $y$-values. Create ordered pairs to plot.
Choose $x$-values and compute the corresponding $y$-values. Create ordered pairs to plot.
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What labels should be included on a coordinate graph of $y$ versus $x$?
What labels should be included on a coordinate graph of $y$ versus $x$?
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Label axes with variable names and units (if given). Proper labeling makes graphs interpretable.
Label axes with variable names and units (if given). Proper labeling makes graphs interpretable.
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Identify the dependent variable in the model $C=3v+10$ where $v$ is number of visits.
Identify the dependent variable in the model $C=3v+10$ where $v$ is number of visits.
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The dependent variable is $C$. The output variable that depends on $v$.
The dependent variable is $C$. The output variable that depends on $v$.
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Identify the independent variable in the model $C=3v+10$ where $v$ is number of visits.
Identify the independent variable in the model $C=3v+10$ where $v$ is number of visits.
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The independent variable is $v$. The input variable that can be chosen.
The independent variable is $v$. The input variable that can be chosen.
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What is the equation for total distance $d$ if you start with $d_0$ and travel at speed $v$ for time $t$?
What is the equation for total distance $d$ if you start with $d_0$ and travel at speed $v$ for time $t$?
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$d=d_0+vt$. Initial distance plus distance traveled.
$d=d_0+vt$. Initial distance plus distance traveled.
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What is the equation for cost $C$ if fixed cost is $50$ and variable cost is $6$ per unit $x$?
What is the equation for cost $C$ if fixed cost is $50$ and variable cost is $6$ per unit $x$?
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$C=6x+50$. Fixed cost plus variable cost per unit.
$C=6x+50$. Fixed cost plus variable cost per unit.
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What is the equation for profit $P$ if revenue is $R$ and cost is $C$?
What is the equation for profit $P$ if revenue is $R$ and cost is $C$?
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$P=R-C$. Revenue minus total costs.
$P=R-C$. Revenue minus total costs.
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What is the equation for revenue $R$ when each item costs $8$ dollars and $x$ items are sold?
What is the equation for revenue $R$ when each item costs $8$ dollars and $x$ items are sold?
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$R=8x$. Price per item times number sold.
$R=8x$. Price per item times number sold.
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What is the equation for taxi cost $C$ with base fare $4$ and $2.5$ dollars per mile $m$?
What is the equation for taxi cost $C$ with base fare $4$ and $2.5$ dollars per mile $m$?
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$C=2.5m+4$. Base fare plus cost per mile.
$C=2.5m+4$. Base fare plus cost per mile.
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What is the equation for total cost $C$ with $10$ dollar membership fee plus $3$ dollars per visit $v$?
What is the equation for total cost $C$ with $10$ dollar membership fee plus $3$ dollars per visit $v$?
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$C=3v+10$. Fixed fee plus cost per visit.
$C=3v+10$. Fixed fee plus cost per visit.
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What is the equation for total pay $P$ with hourly wage $15$ and $h$ hours worked?
What is the equation for total pay $P$ with hourly wage $15$ and $h$ hours worked?
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$P=15h$. Hourly wage times hours worked.
$P=15h$. Hourly wage times hours worked.
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What is the meaning of $b$ in $y=mx+b$ in terms of an initial value?
What is the meaning of $b$ in $y=mx+b$ in terms of an initial value?
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$b$ is the initial value when $x=0$. The $y$-intercept represents the starting value.
$b$ is the initial value when $x=0$. The $y$-intercept represents the starting value.
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Identify the equation modeling “$y$ varies directly with $x$” and $y=-10$ when $x=5$.
Identify the equation modeling “$y$ varies directly with $x$” and $y=-10$ when $x=5$.
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$y=-2x$. Find $k$: $-10=k(5)$, so $k=-2$.
$y=-2x$. Find $k$: $-10=k(5)$, so $k=-2$.
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