Question

Find the \(x\) -intercept and the \(y\) -intercept of the line. Graph the equation. Label the points where the line crosses the axes. $$ x-7 y=21 $$

Short answer

The x-intercept is at the point (21, 0) and the y-intercept is at the point (0, -3).

Step-by-step solution

Find the x-intercept

To find the x-intercept, set \(y\) to 0 in the equation and solve for \(x\). This gives an equation \(x - 7(0) = 21\), so \(x = 21\). Therefore, the x-intercept is at the point (21, 0).

Find the y-intercept

To find the y-intercept, set \(x\) to 0 in the equation and solve for \(y\). This gives an equation \(0 - 7y = 21\), so \(y = -3\). Therefore, the y-intercept is at the point (0, -3).

Graph and label the line

Plot the points (21, 0) and (0, -3) on a graph. These are the points where the line crosses the x and y-axes respectively. Draw the line that passes through these points. This line represents the equation. Be sure to label the points.