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)