Question

drag the red and blue dots along the x-axis and y-axis to graph $2x - 6y = 18$.

Explanation:

Step 1: Find x - intercept

Set \(y = 0\) in \(2x-6y = 18\).
\(2x-6(0)=18\Rightarrow2x = 18\Rightarrow x = 9\).

Step 2: Find y - intercept

Set \(x = 0\) in \(2x-6y = 18\).
\(2(0)-6y=18\Rightarrow - 6y = 18\Rightarrow y=-3\).
We use the x - intercept \((9,0)\) and y - intercept \((0, - 3)\) to graph the line by moving the blue dot (x - intercept) to \((9,0)\) and the red dot (y - intercept) to \((0,-3)\).

Answer:

To graph the equation \(2x - 6y = 18\), we find the x - intercept and y - intercept:

Step 1: Find the x - intercept (set \(y = 0\))

Substitute \(y = 0\) into the equation \(2x-6y = 18\).
We get \(2x-6(0)=18\), which simplifies to \(2x=18\).
Dividing both sides by 2, we have \(x = 9\). So the x - intercept is the point \((9,0)\).

Step 2: Find the y - intercept (set \(x = 0\))

Substitute \(x = 0\) into the equation \(2x - 6y=18\).
We get \(2(0)-6y = 18\), which simplifies to \(- 6y=18\).
Dividing both sides by \(-6\), we have \(y=- 3\). So the y - intercept is the point \((0, - 3)\).

To graph the line, we should drag the red dot (y - intercept) to \((0,-3)\) and the blue dot (x - intercept) to \((9,0)\) on the coordinate plane.