10. Undefined38. T; Alt Ext Angles T; Corr Angles 14. M = 150, average speed of 150 mi/h40. F; Same-Side Int Angles 16. neither 18. M = 1150/2400 ≈ 0.5, average change in elevation is 0.5 m per kilometer /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 Up Substitute 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 = x – 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 – y 1 = m(x – x 1 ) y – (–4) = 6(x – 3) Point-slope form Substitute 6 for m, 3 for x 1, and -4 for y 1. 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 – y 1 = m(x – x 1 ) Point-slope form Use the point (3,-5) to find the slope. Simplify. Substitute for m, 3 for x 1, and 0 for y y = (x - 3) 5 3 y – 0 = (x – 3) 5 3

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)