Question

use intercepts and a checkpoint to graph the linear function below.
8x - 4y = 16

use the graphing tool to graph the linear equation. use the intercepts when drawing the line. if only one intercept exists, use it and another point to draw the line.
click to enlarge graph

Explanation:

Step1: Find x-intercept (y=0)

Substitute \( y = 0 \) into \( 8x - 4y = 16 \):
\( 8x - 4(0) = 16 \)
\( 8x = 16 \)
\( x = \frac{16}{8} = 2 \)
So x-intercept is \( (2, 0) \).

Step2: Find y-intercept (x=0)

Substitute \( x = 0 \) into \( 8x - 4y = 16 \):
\( 8(0) - 4y = 16 \)
\( -4y = 16 \)
\( y = \frac{16}{-4} = -4 \)
So y-intercept is \( (0, -4) \).

Step3: Find a checkpoint (e.g., x=1)

Substitute \( x = 1 \) into \( 8x - 4y = 16 \):
\( 8(1) - 4y = 16 \)
\( 8 - 4y = 16 \)
\( -4y = 16 - 8 = 8 \)
\( y = \frac{8}{-4} = -2 \)
Checkpoint is \( (1, -2) \).

Plot \( (2, 0) \), \( (0, -4) \), and \( (1, -2) \), then draw a line through them.

Answer:

To graph \( 8x - 4y = 16 \):

• x-intercept: \( (2, 0) \) (set \( y = 0 \), solve \( 8x = 16 \Rightarrow x = 2 \))
• y-intercept: \( (0, -4) \) (set \( x = 0 \), solve \( -4y = 16 \Rightarrow y = -4 \))
• Checkpoint (e.g., \( x = 1 \)): \( (1, -2) \) (substitute \( x = 1 \), solve \( 8 - 4y = 16 \Rightarrow y = -2 \))

Plot these points and draw a line through them. The line passes through \( (2, 0) \), \( (0, -4) \), and \( (1, -2) \).