Linear Equations - SAT Math
Card 0 of 116
What is the formula for slope (m) between two points $(x_1, y_1)$ and $(x_2, y_2)$?
What is the formula for slope (m) between two points $(x_1, y_1)$ and $(x_2, y_2)$?
$m=\frac{y_2-y_1}{x_2-x_1}$.
$m=\frac{y_2-y_1}{x_2-x_1}$.
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What is the slope-intercept form of a line?
What is the slope-intercept form of a line?
$y=mx+b$.
$y=mx+b$.
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What is the point-slope form of a line?
What is the point-slope form of a line?
$y-y_1=m(x-x_1)$.
$y-y_1=m(x-x_1)$.
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What is the standard form of a line?
What is the standard form of a line?
$Ax+By=C$, where A, B, and C are integers and A ≥ 0.
$Ax+By=C$, where A, B, and C are integers and A ≥ 0.
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How do you find y-intercept of a line given slope and a point?
How do you find y-intercept of a line given slope and a point?
Substitute the point (x, y) and slope m into $y=mx+b$ to solve for b.
Substitute the point (x, y) and slope m into $y=mx+b$ to solve for b.
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How can you determine parallel lines in slope-intercept form?
How can you determine parallel lines in slope-intercept form?
They have the same slope $(m_1 = m_2).$
They have the same slope $(m_1 = m_2).$
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How can you determine perpendicular lines in slope-intercept form?
How can you determine perpendicular lines in slope-intercept form?
Their slopes are negative reciprocals: $m_1 m_2 = -1$.
Their slopes are negative reciprocals: $m_1 m_2 = -1$.
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Formula for x-intercept of a line given $y=mx+b$.
Formula for x-intercept of a line given $y=mx+b$.
Set $y=0$ ⇒ 0 = mx + b ⇒ $x=-\frac{b}{m}$.
Set $y=0$ ⇒ 0 = mx + b ⇒ $x=-\frac{b}{m}$.
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What is the meaning of slope in a linear model?
What is the meaning of slope in a linear model?
Rate of change of y with respect to x; how much y increases when x increases by 1.
Rate of change of y with respect to x; how much y increases when x increases by 1.
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What is the meaning of y-intercept in a linear model?
What is the meaning of y-intercept in a linear model?
The value of y when $x=0$.
The value of y when $x=0$.
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What does it mean if two linear equations have no solution?
What does it mean if two linear equations have no solution?
Their lines are parallel and distinct (same slope, different intercepts).
Their lines are parallel and distinct (same slope, different intercepts).
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What does it mean if two linear equations have infinitely many solutions?
What does it mean if two linear equations have infinitely many solutions?
They represent the same line (same slope and y-intercept).
They represent the same line (same slope and y-intercept).
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When solving Ax + B = Cx + D, what’s the first algebraic step?
When solving Ax + B = Cx + D, what’s the first algebraic step?
Combine like terms: bring x-terms to one side and constants to the other.
Combine like terms: bring x-terms to one side and constants to the other.
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What does the slope m = 0 represent?
What does the slope m = 0 represent?
A horizontal line; no change in y as x changes.
A horizontal line; no change in y as x changes.
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What kind of line has an undefined slope?
What kind of line has an undefined slope?
A vertical line ($x=\text{constant}$).
A vertical line ($x=\text{constant}$).
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How can you check whether (x, y) is a solution to a linear equation?
How can you check whether (x, y) is a solution to a linear equation?
Substitute x and y into the equation and see if it makes a true statement.
Substitute x and y into the equation and see if it makes a true statement.
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What is the formula for distance between two points $(x_1, y_1)$ and $(x_2, y_2)$?
What is the formula for distance between two points $(x_1, y_1)$ and $(x_2, y_2)$?
$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
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How do you find the midpoint between $(x_1, y_1)$ and $(x_2, y_2)$?
How do you find the midpoint between $(x_1, y_1)$ and $(x_2, y_2)$?
$((x_1 + x_2)/2, (y_1 + y_2)/2).$
$((x_1 + x_2)/2, (y_1 + y_2)/2).$
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What are the steps to find equation of a line given two points.
What are the steps to find equation of a line given two points.
- Find slope; 2) use point-slope form; 3) simplify to desired form.
- Find slope; 2) use point-slope form; 3) simplify to desired form.
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What’s the algebraic goal when solving a linear equation?
What’s the algebraic goal when solving a linear equation?
Isolate the variable on one side of the equation.
Isolate the variable on one side of the equation.
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