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Part I.
5 Model Problems Answered step by step
Part II.
Practice Problems
Part III.
Solutions fully worked out
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Model Problem 1 )
1) What is the equation of a line with a slope of 3 that goes through the point (2,8) ?
Step 1) substitute slope into equation
y =mx + b
y = 3x + b
Step 2) substitute (2,8) into equation
8 = 3(2) +b
Step 3) solve for b
8=6+b
2=b
Step 4) Insert B into equation
y = 3x + 2
Model problem 2 )
What is an equation for the line that passes through the coordinates (4,5) and (8, 3)?
1) Calculate Slope
53 2
1


4  8 4
2
2) Plug it into the slope intercept formula:
y=

1
x
2
+b
3) Plug the x and y given in the question into the slope intercept formula
1
5   (4)  b
2
4) Solve for b
1
5   (4)  b
2
5  2b
2 +2
7b
5) Rewrite equation in slope intercept form
1
y   x7
2
Model Problem 3)
Write the equation of a line that is parallel to y = 2x + 3 and passes through the points (6,2).
Step 1) plug slope the slope intercept formula:
y = mx + b
y = 2x + b
2) Plug the x and y given in the question into the slope intercept formula
2 = 2(6) + b
3) Solve for b
2  12  b
12  12
10  b
5) Rewrite equation with only slope and y-intercept
y = 2x – 10
Model Problem 4)
Write the equation of a line that is perpendicular to y = ½x – 6 and passes
through the point (6,4) ?
Step 1) find the negative reciprocal of the slope
Slope =
1
2
Negative reciprocal
—2
2) Plug the x and y given in the question into slope intercept formula
4= -2(6) + b
3) Solve for b
4  12  b
12  12
16  b
4) Rewrite equation in slope intercept form
y = -2x + 16
Model Problem 5)
Write the equation of the perpendicular bisector that goes through the line
segment with end points of
A (2,1) and B (6, -3)
Step 1) Find the slope of the line
segment using the points given
Step 2) Find the slope of a line that
is perpendicular to the original line
segment.
1  3 1  3 4


 1
26
4 4
1 1
1     1
1 1
Step 3) Find the midpoint of the
original two points
 2  6 1  3   8 1  3 
,

 ,

2
2
2
2

 

 2 
 4,    4, 1
 2 
Step 4) Use the midpoint and new
slope to solve for the y-intercept
y = mx + b
y  1x  b
1  1 4   b
1  4  b
4  4
5  b
Step 5) Write the equation using
new slope and y-intercept
y  x 5
Mixed Review on Linear Equations
1) What is the equation of a line with a slope of 3 that goes through the point (2,8)? (see Model
Problem 1 if you’re stuck)
2) What is the equation of a line through the point (1,3) that has a slope of -2?
3) What is the equation of a line through the point (-2, 3) that has a slope of 4?
4) What is the equation of a line through the point (1,3) that has a slope of -2?
5) What is an equation for the line that passes through the coordinates (4,5) and (8, 3)? (see
Model Problem 2 if you’re stuck)
6) What is an equation for the line that passes through the coordinates (-1,2) and (7,6) ?
7) Find the equation of the line that passes through the points (1,1) and (3,5)?
8) Write the equation of a line that is parallel to y = 2x + 3 and passes through the points (6,2).(See
Model Problem 3 if you’re stuck)
9) Find the equation of line parallel to y = 2x +7 and that goes through the point (4 , 12) ?
10)Find the equation of a line parallel to y =4x + 12 that goes through the point (1,9) ?
11) Write the equation of a line that is perpendicular to y = ½x – 6 that passes through
the point (6,4) ? (See Model Problem 4 if you’re stuck)
12) Write the equation of a line that is perpendicular to y = 
(6,7) ?
3
x – 3 that passes through the point
2
13) Write the equation of a line that is perpendicular to y = -2x + 4 that passes through the
point (8 , 8 ) .
14)Write the equation of the perpendicular bisector that goes through the line segment with
end points of A (2,1) and B (6, -3) (See Model Problem 5 if you’re stuck)
15) Write the equation of the perpendicular bisector that goes through the line segment with
end points of A (-1, -2) and B (-2, -8)
16) Write the equation of the perpendicular bisector that goes through the line segment with
end points of A (-1, 1) and B (7,5)
Answer Key
1)
2)
3)
4)
y = 3x + 2
y = - 2x + 5
y = 4x + 11
y = -2x + 5
1
x+7
2
1
6) y = x + 2.5
2
5) y = 
7)
8)
9)
10)
11)
y = 2x -1
y = 2x -10
y = 2x +4
y = 4x + 5
y = -2x + 16
2
x+3
3
1
13) y = x + 4
2
12) y =
14) y = x -5
1
 5.25
6
4
16) y = x – 6
3
4
91
17) y =  x 
5
100
15) y = 