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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