Question

1. two lines that are perpendicular lines have ...

a slope that is opposite reciprocals
b slope that is the same
c no slope
d none of the above

1. write an equation for a line parallel to the line $y = \frac{1}{3}x - 4$ through $(-3, 2)$

a $y = \frac{2}{3}x +3$
b $y = -\frac{1}{3}x + 3$
c $y = \frac{1}{3}x + 3$
d $y = -\frac{5}{3}x + 3$

1. write an equation of a line that passes through the point $(5,-1)$ and is parallel to the line $y = -\frac{3}{5}x -3$

a $y = -\frac{3}{5}x -2$
b $y = \frac{3}{5}x + 2$
c $y = -\frac{3}{5}x + 2$
d $y = \frac{5}{3} + 2$

Explanation:

Step 1 (Q8): Recall perpendicular line rule

Perpendicular lines have slopes that are opposite reciprocals (their product is $-1$).

Step 2 (Q9): Identify parallel line slope

Parallel lines have equal slopes. Given $y=\frac{1}{3}x-4$, slope $m=\frac{1}{3}$. Use point-slope form $y-y_1=m(x-x_1)$ with $(-3,2)$:
$y-2=\frac{1}{3}(x+3)$
Simplify: $y=\frac{1}{3}x + 1 + 2 = \frac{1}{3}x + 3$

Step 3 (Q10): Identify parallel line slope

Parallel lines have equal slopes. Given $y=-\frac{3}{5}x-3$, slope $m=-\frac{3}{5}$. Use point-slope form $y-y_1=m(x-x_1)$ with $(5,-1)$:
$y+1=-\frac{3}{5}(x-5)$
Simplify: $y=-\frac{3}{5}x + 3 - 1 = -\frac{3}{5}x + 2$

Answer:

1. A. Slope that is opposite reciprocals
2. C. $y = (1/3)x + 3$
3. C. $y = (-3/5)x + 2$