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Equations of a Line Test
About Equations of a Line:

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)


y=-2x+4

b)


y=(4/5)x+1
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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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