10. Undefined 38. T; Alt Ext Angles

12. -1 39. T; Corr Angles

14. M = 150, average speed of 150 mi/h 40. F; Same-Side Int Angles

16. neither

18. M = 1150/2400 ≈ 0.5, average change in elevation is 0.5 m per kilometer

20. -1

22. -4/9

24. Lines have same slope so they are either parallel or same line

26. A

28. C

29. JK is vertical line

30. JK is horizontal line

31. Slope AB = slope CD = 1 Distance formula for the four sides = 6√2

Slope BC = slope AD = -1

A. opposite sides have same slope so parallel

B. slopes of 2 consecutive sides are opp. reciprocals so consecutive sides are

C. All sides have the same length so they are

Warm UpSubstitute the given values of m, x, and y into the equation y = mx + b and solve for b.

1. m = 2, x = 3, and y = 0

Solve each equation for y.

3. y – 6x = 9

2. m = –1, x = 5, and y = –4

b = –6

b = 1

4. 4x – 2y = 8

y = 6x + 9

y = 2x – 4

The equation of a line can be written in many different forms. The point-slope and slope-intercept forms of a line are equivalent. Because the slope of a vertical line is undefined, these forms cannot be used to write the equation of a vertical line.

Example 1A:Write the equation of each line in the given form.

the line with slope 6 through (3, –4) in point-slope form

y – y1 = m(x – x1)

y – (–4) = 6(x – 3)

Point-slope form

Substitute 6 for m, 3 for x1, and -4 for y1.

y + 4 = 6(x – 3)

Example 1B:

Write the equation of each line in the given form.

the line through (–1, 0) and (1, 2) in slope-intercept form

y = mx + b

0 = 1(-1) + b

1 = b

y = x + 1

Slope-intercept form

Find the slope.

Substitute 1 for m, -1 for x, and 0 for y.

Write in slope-intercept form using m = 1 and b = 1.

Example 1C:

Write the equation of each line in the given form.

the line with the x-intercept 3 and y-intercept –5 in point slope form

y – y1 = m(x – x1) Point-slope form

Use the point (3,-5) to find the slope.

Simplify.

Substitute for m, 3 for x1, and 0 for y1.

53

y = (x - 3)53

y – 0 = (x – 3)53

Example 2a

Graph each line.

y = 2x – 3

The equation is given in the

slope-intercept form, with a

slope of and a y-intercept

of –3. Plot the point (0, –3)

and then rise 2 and run 1 to

find another point. Draw the

line containing the points.

(0, –3)

rise 2

run 1

Example 2b

Graph each line.

The equation is given in the

point-slope form, with a slope

of through the point (–2, 1).

Plot the point (–2, 1)and then

rise –2 and run 3 to find

another point. Draw the line

containing the points.

(–2, 1)

run 3

rise –2

Example 2c

Graph each line.

y = –4

The equation is given in the form

of a horizontal line with a

y-intercept of –4.

The equation tells you that the

y-coordinate of every point on the

line is –4. Draw the horizontal line

through (0, –4).

(0, –4)