Question

graph $3x - 4y = 24$.
youre almost there
there are still more parts
give it another try!

Explanation:

Step1: Find x-intercept (y=0)

Set \( y = 0 \) in \( 3x - 4y = 24 \):
\( 3x - 4(0) = 24 \)
\( 3x = 24 \)
\( x = 8 \). So x-intercept is \( (8, 0) \)? Wait, no, wait—wait, the graph has a horizontal line at y=5? Wait, no, maybe I misread. Wait, the equation is \( 3x - 4y = 24 \). Let's solve for y to get slope-intercept form.

Step2: Solve for y (slope-intercept form)

\( 3x - 4y = 24 \)
Subtract \( 3x \): \( -4y = -3x + 24 \)
Divide by -4: \( y = \frac{3}{4}x - 6 \).

Wait, the graph in the image is a horizontal line (y=5), which doesn't match. So maybe the graph is incorrect, but to graph \( 3x - 4y = 24 \) properly:

Step3: Find x-intercept (y=0)

\( 3x - 4(0) = 24 \Rightarrow x = 8 \), so point \( (8, 0) \).

Step4: Find y-intercept (x=0)

\( 3(0) - 4y = 24 \Rightarrow -4y = 24 \Rightarrow y = -6 \), so point \( (0, -6) \).

Plot \( (8, 0) \) and \( (0, -6) \), then draw a line through them.

Answer:

To graph \( 3x - 4y = 24 \):

1. Find x-intercept (set \( y = 0 \)): \( 3x = 24 \Rightarrow x = 8 \) (point: \( (8, 0) \)).
2. Find y-intercept (set \( x = 0 \)): \( -4y = 24 \Rightarrow y = -6 \) (point: \( (0, -6) \)).
3. Plot these two points and draw a straight line through them.

(Note: The provided graph in the image is incorrect for \( 3x - 4y = 24 \); the correct line has a slope of \( \frac{3}{4} \) and passes through \( (8, 0) \) and \( (0, -6) \).)