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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
2 x + b
3) Plug the x and y given in the question into the slope intercept formula
15 (4)
2b
4) Solve for b
15 (4)
2
5 2
2 +2
7
b
b
b
5) Rewrite equation in slope intercept form
17
2y x
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
12 12
10
b
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
12 12
16
b
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
1 3 1 3 41
2 6 4 4
Step 2) Find the slope of a line that
is perpendicular to the original line
segment.
1 11 1
1 1
Step 3) Find the midpoint of the
original two points
2 6 1 3 8 1 3, ,
2 2 2 2
24, 4, 1
2
Step 4) Use the midpoint and new
slope to solve for the y-intercept
y = mx + b
1
1 1 4
1 4
4 4
5
y x b
b
b
b
Step 5) Write the equation using
new slope and y-intercept
5y x
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 = 3
2 x – 3 that passes through the point
(6,7) ?
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) y = 3x + 2
2) y = - 2x + 5
3) y = 4x + 11
4) y = -2x + 5
5) y = 1
2 x + 7
6) y = 1
2x + 2.5
7) y = 2x -1
8) y = 2x -10
9) y = 2x +4
10) y = 4x + 5
11) y = -2x + 16
12) y = 2
3x + 3
13) y = 1
2x + 4
14) y = x -5
15) y =1
5.256
16) y = 4
3x – 6
17) y = 4 91
5 100x