Question

1. which equation represents a line that is perpendicular to the line with the equation $y = \frac{3}{4}x + 5$?

a. $y = -\frac{4}{3}x + 2$
b. $y = \frac{3}{4}x + 7$
c. $y = \frac{4}{3}x - 3$
d. $y = -\frac{3}{4}x - 5$

1. consider the following line.

graph of a line on a coordinate plane
a. what is the slope of the given line?
b. graph a line that is parallel to the given line in the same coordinate plane.
what is the slope of your line in part (b)?
line \\( \ell \\) is represented by the table.

x	y
-4	0
0	2
3	4

line \\( m \\) is represented by the equation $y = \frac{2}{3}x - 2$
are lines \\( \ell \\) and \\( m \\) parallel? explain how you know.

Explanation:

Step1: Find slope of line \( l \)

Use slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Take points \((-3, 0)\) and \((0, 2)\):
\( m_l = \frac{2 - 0}{0 - (-3)} = \frac{2}{3} \).

Step2: Find slope of line \( m \)

Line \( m \) has equation \( y = \frac{2}{3}x - 2 \). In slope - intercept form \( y = mx + b \), slope \( m_m = \frac{2}{3} \).

Step3: Compare slopes

Parallel lines have equal slopes. Since \( m_l = \frac{2}{3} \) and \( m_m = \frac{2}{3} \), their slopes are equal.

Answer:

Yes, lines \( l \) and \( m \) are parallel because they have the same slope (\(\frac{2}{3}\) for both).