Question

Find the \(x\) -intercept and the \(y\) -intercept of the line. Graph the equation. Label the points where the line crosses the axes. $$ y=-6+3 x $$

Short answer

The x-intercept is (2,0) and the y-intercept is (0,-6).

Step-by-step solution

Calculate the X-Intercept

Set \(y = 0\) in the equation and solve for \(x\). The equation becomes: \(0 = -6 + 3x\). If you add 6 to each side and then divide each side by 3, you will find that \(x = 2\). So, the x-intercept of the line is (2,0).

Calculate the Y-Intercept

Set \(x = 0\) in the equation and solve for \(y\). The equation becomes: \(y = -6 + 3 * 0\), which simplifies to \(y = -6\). So, the y-intercept of the line is (0,-6).

Graph the Line and Label the Points

Plot the points (2,0) and (0,-6) on the graph. Draw a line through these points. Label the points where the line crosses the axes.