Questions: What are the x-and y-intercepts of -6x+4y=96? Enter your answers in the boxes. x-intercept: y-intercept:

Transcript text: What are the $x$-and $y$-intercepts of $-6 x+4 y=96$ ? Enter your answers in the boxes. $x$-intercept: $\square$ $y$-intercept: $\square$ $\square$

Solution

Solution Steps

To find the intercepts of the equation $-6x + 4y = 96$, we need to determine where the line crosses the x-axis and y-axis. For the x-intercept, set $y = 0$ and solve for $x$. For the y-intercept, set $x = 0$ and solve for $y$.

Step 1: Find the x-intercept

To find the x-intercept, we set $y = 0$ in the equation $-6x + 4y = 96$: \[ -6x + 4(0) = 96 \implies -6x = 96 \implies x = -\frac{96}{6} = -16 \]

Step 2: Find the y-intercept

To find the y-intercept, we set $x = 0$ in the equation $-6x + 4y = 96$: \[ -6(0) + 4y = 96 \implies 4y = 96 \implies y = \frac{96}{4} = 24 \]