Question

Find the \(x\) -intercept and the \(y\) -intercept of the line. Graph the equation. Label the points where the line crosses the axes. $$ -4 x+3 y=24 $$

Short answer

The x-intercept of the line is 6, and the y-intercept is 8.

Step-by-step solution

Find the x-intercept

To find the x-intercept, set \(y = 0\) in the equation and solve for \(x\). So,\[-4x + 3 * 0 = 24 \-4x = 24 \x = - \frac{24}{-4} = 6\]So, the x-intercept is 6.

Find the y-intercept

To find the y-intercept, set \(x = 0\) in the equation and solve for \(y\). So,\[-4 * 0 + 3y = 24 \3y = 24 \y = \frac{24}{3} = 8\]So, the y-intercept is 8.

Graph the equation

Plot the line using the x-intercept (6,0) and the y-intercept (0,8). The line crossing these points represents the equation \(-4x + 3y = 24\)