Question

topic 6: writing linear equations (given a point and slope, or two points)

1. (-4, -7); slope = 3
2. (8, -9); slope = -5/4
3. (-3, -9) and (4, -2)
4. (-2, 7) and (6, -5)

topic 7: parallel & perpendicular lines

1. describe the slopes of parallel lines.
2. describe the slopes of perpendicular lines.
3. which line is parallel to the line 5x - 2y = 18?

a. $y = \frac{2}{5}x + 1$
b. $y = -\frac{2}{5}x - 7$
c. $y = \frac{5}{2}x - 4$
d. $y = -\frac{5}{2}x + 2$

1. which line is perpendicular to the line $y = -3x + 2$

a. $3x + y = 4$
b. $x + 3y = 24$
c. $3x - y = 5$
d. $x - 3y = 3$

1. write an equation that is parallel to $y = -4x + 5$ and passes through the point (-2, -1).
2. write an equation that is perpendicular to $3x - 5y = 5$ and passes through the point (9, -14).

Explanation:

Step1: Q22: Define parallel slopes

Parallel lines have identical slopes.

Step2: Q23: Define perpendicular slopes

Perpendicular slopes are negative reciprocals (product = -1).

Step3: Q24: Find slope of given line

Rewrite $5x-2y=18$ to slope-intercept form:
$ -2y = -5x + 18 $
$ y = \frac{5}{2}x - 9 $
Slope $m=\frac{5}{2}$. Parallel lines match this slope.

Step4: Q25: Find perpendicular slope

Given $y=-3x+2$, slope $m=-3$. Perpendicular slope is $\frac{1}{3}$. Rewrite options to slope-intercept:
A. $y=-3x+4$ (slope=-3)
B. $y=-\frac{1}{3}x+8$ (slope=$-\frac{1}{3}$)
C. $y=3x-5$ (slope=3)
D. $y=\frac{1}{3}x-1$ (slope=$\frac{1}{3}$)

Step5: Q26: Write parallel line equation

Given $y=-4x+5$, parallel slope $m=-4$. Use point $(-2,-1)$ in point-slope form:
$ y - (-1) = -4(x - (-2)) $
$ y + 1 = -4x - 8 $
$ y = -4x - 9 $

Step6: Q27: Write perpendicular line equation

Rewrite $3x-5y=5$ to slope-intercept:
$ -5y = -3x + 5 $
$ y = \frac{3}{5}x - 1 $
Perpendicular slope $m=-\frac{5}{3}$. Use point $(9,-14)$:
$ y - (-14) = -\frac{5}{3}(x - 9) $
$ y + 14 = -\frac{5}{3}x + 15 $
$ y = -\frac{5}{3}x + 1 $

Answer:

1. Parallel lines have equal slopes.
2. Perpendicular lines have slopes that are negative reciprocals (their product is -1).
3. C. $y = \frac{5}{2}x - 4$
4. D. $x - 3y = 3$
5. $y = -4x - 9$
6. $y = -\frac{5}{3}x + 1$