Question

multiple-choice question is $y = -\frac{4}{3}x + 18$ parallel to $4x - 3y = 18$ yes no

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have equal slopes. So, we need to find the slopes of both lines.

Step2: Find slope of first line

The first line is \( y = -\frac{4}{3}x + 18 \), which is in slope - intercept form \( y=mx + b \), where \( m \) is the slope. So, the slope of \( y = -\frac{4}{3}x + 18 \) is \( m_1=-\frac{4}{3} \).

Step3: Rewrite second line in slope - intercept form

We have the second line \( 4x-3y = 18 \). Let's solve for \( y \):
Subtract \( 4x \) from both sides: \( - 3y=-4x + 18 \)
Divide both sides by \( - 3 \): \( y=\frac{4}{3}x-6 \)
In slope - intercept form \( y = mx + b \), the slope of this line \( m_2=\frac{4}{3} \)

Step4: Compare the slopes

We have \( m_1 =-\frac{4}{3} \) and \( m_2=\frac{4}{3} \). Since \( m_1
eq m_2 \), the lines are not parallel.

Answer:

no