# Graphing and Equations of Lines

Find the slope and y-intercept of the line represented by each of the following equations.

See attached file for full problem description.

Find the slope and y-intercept of the line represented by each of the following equations.

12.

Or 3Y = 2X - 6

Or Y = (2/3) X - 2

Slope = 2/3

y-intercept = -2

Write the equation of the line with given slope and y-intercept. Then graph each line using the slope and y-intercept.

16. Slope: -2; y-intercept: (0, 4)

y = -2x + 4

At x = 1, y = 2

At x = 0, y = 4

+y

9

8

7

6

5

4

3

2

1

-x -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 +x

-1

-2

-3

-4

-5

-6

-7

-8

-9

-y

18. Slope: 5; y-intercept: (0, -2). y = 5x - 2

At x = 0, y = -2

At y = 0, x = 0.4

+y

9

8

7

6

5

4

3

2

1

-x -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 +x

-1

-2

-3

-4

-5

-6

-7

-8

-9

-y

20. Slope: y-intercept: (0, 8). y = -(3/4)x + 8

At x = 0, y = 8

At y = 0, x = 32/3 = 10.67

+y

9

8

7

6

5

4

3

2

1

-x -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 +x

-1

-2

-3

-4

-5

-6

-7

-8

-9

-y

In exercises 25 to 32, match the graph with one of the following equations.

(a) y= 2x (b) y= x + 1 (c) y= -x + 3 (d) y = 2x + 1

(e) y=-3x - 2 (f ) y= + 1 (g) y=- (h) y = -4x

26. Since the line cuts the y-axis below the origin, the y-intercept will be negative. There is only one option with a negative y-intercept, which is (e)

+y

9

8

7

6

5

4

3

2

1

-x -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 +x

-1

-2

-3

-4

-5

-6

-7

-8

-9

-y

28. In exercises 25 to 32, match the graph with one of the following equations.

(a) y= 2x (b) y= x + 1 (c) y= -x + 3 (d) y = 2x + 1

(e) y=-3x - 2 (f ) y= + 1 (g) y=- (h) y = -4x

Since the line cuts the y-axis below the origin, the y-intercept will be negative. There is only one option with a negative y-intercept, which is (e)

+y

9

8

7

6

5

4

3

2

1

-x -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 +x

-1

-2

-3

-4

-5

-6

-7

-8

-9

-y

In exercises 25 to 32, match the graph with one of the following equations.

(a) y= 2x (b) y= x + 1 (c) y= -x + 3 (d) y = 2x + 1

(e) y=-3x - 2 (f ) y= + 1 (g) y=- (h) y = -4x

30. b is the correct answer because the line cuts the y-axis at 1 (y-intercept = 1) and the slope is about 450 (m = 1)

+y

9

8

7

6

5

4

3

2

1

-x -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 +x

-1

-2

-3

-4

-5

-6

-7

-8

-9

-y

In exercises 25 to 32, match the graph with one of the following equations.

(a) y= 2x (b) y= x + 1 (c) y= -x + 3 (d) y = 2x + 1

(e) y=-3x - 2 (f ) y= + 1 (g) y=- (h) y = -4x

32. a is the correct answer because the line passes through the origin (so the y-intercept is zero) and the slope is positive and more than 1.

9

8

7

6

5

4

3

2

1

-x -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 +x

-1

-2

-3

-4

-5

-6

-7

-8

-9

-y

#### Solution Summary

Graphing and Equations of Lines are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.