Linear Equations and Slope-Intercept Form Quiz

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Questions and Answers

What is the slope-intercept form of the equation of a line that passes through (3, 4) with a slope of -2?

$y = 2x + 10$
$y = 2x - 10$
$y = -2x - 10$ (correct)
$y = -2x + 10$

Which is an equation of the line that passes through (1, 5) and (4, 11)?

$y = 3x + 2$
$y = 2x - 3$
$y = 2x + 3$ (correct)
$y = 3x - 2$

What is an equation of the line through (0, 2) with slope $-\frac{1}{3}$?

$3x + y = 2$
$x + 3y = 2$
$y = -\frac{1}{3}x + 2$ (correct)
$x - 3y = 2$

Which is an equation of the line with slope 4 and passes through (-3, 2)?

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What is the equation of the line through (5, 3) with a slope of 0?

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Flashcards

Slope-intercept form through (3,4) with slope -2

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Given a point (3, 4) and slope -2, the equation is y = -2x + b. Solving for b gives y = -2x + 10.

Equation of line through (1,5) and (4,11)

To find the equation, first find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). Using points (1, 5) and (4, 11), m = (11-5)/(4-1) = 2. Now use point-slope form y - y1 = m(x - x1) and one of the points to find the equation.

Equation of line through (0,2) with slope -1/3

Using slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Given the slope is -1/3 and goes through (0, 2), the equation is y = (-1/3)x + 2.

Equation of line with slope 4 through (-3,2)

Given slope 4, we have y = 4x + b using point-slope form. Then substitute (-3,2), 2 = 4*(-3) + b. Solve for b, yielding y = 4x + 14.

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Line through (5, 3) with slope 0

A horizontal line has a slope of 0. The equation of a horizontal line through any point (x, y) is y = constant. In this case, y=3.

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Study Notes

Slope-Intercept Form

The slope-intercept form of a line that passes through (3, 4) with a slope of -2 is y = -2x + b, where b is the y-intercept.

Equations of Lines

The equation of the line that passes through (1, 5) and (4, 11) is y = 2x + 3.
The equation of the line through (0, 2) with slope $-\frac{1}{3}$ is y = $-\frac{1}{3}$x + 2.
The equation of the line with slope 4 and passes through (-3, 2) is y = 4x + 14.
The equation of the line through (5, 3) with a slope of 0 is y = 3.