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Equations of a Line Test

Although we see point-slope and standard form, an equation is usually written in slope-intercept form: y = mx + b. This form allows us to quickly identify the slope (m) and y-intercept (0,b) from looking at the equation. We can manipulate the equation into this format, by solving for y.

Test Objectives:

•Demonstrate the ability to write the equation of a line in standard form

•Demonstrate the ability to write the equation of a line in slope-intercept form

•Demonstrate the ability to write the equation of a line in point-slope form

Equations of a Line Test:

#1:

Instructions: Write the slope-intercept form of the equation of each line, given the slope and y-intercept.

a) y-intercept = -2

 slope = - 2 5

b) y-intercept = 1

 slope = 3 4

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#2:

Instructions: Write the slope-intercept form of the equation of each line, given the slope and y-intercept.

a) y-intercept = 3

 slope = - 5 4

b) y-intercept = 5

slope = -6

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#3:

Instructions: Graph each line.

a) y = -2x + 4

b)

 y = 4x + 1 5

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#4:

Instructions: Write each equation using point-slope form, then solve for y and place the equation in slope-intercept form.

a) through (-5,3) : slope = 2

b) through (-1,2) : slope = -3

c) through (0,-5) and (5,2)

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#5:

Instructions: Write the standard form of the equation of the line.

a)

 y = -7x + 1 3

b)

 y = 1x + 3 5

c)

 y = -9x + 6 5

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Written Solutions:

#1:

Solution:

a)

 y = -2x - 2 5

b)

 y = 3x + 1 4

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#2:

Solution:

a)

 y = -5x + 3 4

b)

y = -6x + 5

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#3:

Solution:

a)

b)

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#4:

Solution:

a)

point-slope form: y - 3 = 2(x - (-5))
slope-intercept form: y = 2x + 13

b)

point-slope form: y - 2 = -3(x - (-1))
slope-intercept form: y = -3x - 1

c)

 point-slope form: y - 2 = 7 (x - 5) 5

 slope - intercept form: y = 7x -  5 5

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#5:

Solution:

a) 7x + 3y = 3

b) x - 5y = -15

c) 9x + 5y = 30

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