Questions: Find the x-intercept and y-intercept of the line. 7x-4y=28 x-intercept: y-intercept:

Transcript text: Find the $x$-intercept and $y$-intercept of the line. \[ 7 x-4 y=28 \] x -intercept: $\square$ y -intercept: $\square$

Solution

To find the intercepts of the line given by the equation $7x - 4y = 28$:

Step 1: Find the $x$-intercept

To find the $x$-intercept, we set $y = 0$ in the equation $7x - 4y = 28$:

\[ 7x - 4(0) = 28 \implies 7x = 28 \implies x = \frac{28}{7} = 4 \]

Thus, the $x$-intercept is $4$.

Step 2: Find the $y$-intercept

To find the $y$-intercept, we set $x = 0$ in the equation $7x - 4y = 28$:

\[ 7(0) - 4y = 28 \implies -4y = 28 \implies y = \frac{28}{-4} = -7 \]

Thus, the $y$-intercept is $-7$.

The $x$-intercept is $\boxed{4}$ and the $y$-intercept is $\boxed{-7}$.

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