Question

use intercepts and a checkpoint to graph the linear function below.
6x - y = 12

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

To find the x - intercept, set \(y = 0\) in the equation \(6x-y = 12\).
Substitute \(y = 0\) into the equation: \(6x-0=12\), which simplifies to \(6x = 12\).
Divide both sides by 6: \(x=\frac{12}{6}=2\). So the x - intercept is \((2,0)\).

Step2: Find y - intercept

To find the y - intercept, set \(x = 0\) in the equation \(6x - y=12\).
Substitute \(x = 0\) into the equation: \(6(0)-y = 12\), which simplifies to \(-y=12\) or \(y=- 12\). So the y - intercept is \((0,-12)\).

Step3: Find a checkpoint (optional, but to verify)

Let's choose \(x = 1\). Substitute \(x = 1\) into the equation \(6x-y = 12\).
We get \(6(1)-y = 12\), which is \(6 - y=12\).
Subtract 6 from both sides: \(-y=12 - 6=6\), so \(y=-6\). The checkpoint is \((1,-6)\).

Now, to graph the line, plot the x - intercept \((2,0)\), the y - intercept \((0,-12)\) (and the checkpoint \((1, - 6)\) if needed) and draw a straight line through these points.

Answer:

The x - intercept is \((2,0)\), the y - intercept is \((0,-12)\), and a checkpoint is \((1,-6)\). The line can be graphed by plotting these points and drawing a straight line through them.