Question

part ii: spiral

1. which two lines are parallel? explain.

(a) $y = 3x + 2$
$y = 2x + 2$
(b) $y = 3x - 4$
$y = x + 5$
(c) $y = x$
$y = 5$
(d) $y = 0$
$y = 2$

1. points $(-3,8)$ and $(0,5)$ are on a line. which equation represents a line that is parallel to this line? justify your answer.

(a) $y = 2x - 8$
(b) $y = x - 5$
(c) $y = -x + 5$
(d) $y = -2x + 8$

Explanation:

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Question 6

Step1: Recall parallel line rule

Parallel lines have equal slopes.

Step2: Analyze each option

• (A): Slopes $3$ and $2$ (not equal)
• (B): Slopes $3$ and $1$ (not equal)
• (C): Slopes $1$ and $0$ (not equal)
• (D): $y=0$ and $y=2$ are horizontal lines, both have slope $0$ (equal slopes)

Step1: Calculate slope of given line

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{5-8}{0-(-3)}=\frac{-3}{3}=-1$

Step2: Match slope to options

Parallel lines have equal slopes; find the option with slope $-1$.

• (A): Slope $2$
• (B): Slope $1$
• (C): Slope $-1$
• (D): Slope $-2$

Answer:

D. $y=0$, $y=2$
Parallel lines have identical slopes; both lines in option D are horizontal with a slope of 0, so they are parallel.

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Question 7