Questions: Find the x-intercept and y-intercept of the line. 3x + 2y = -12 x-intercept: y-intercept:

Transcript text: Find the $x$-intercept and $y$-intercept of the line. \[ 3 x+2 y=-12 \] $x$-intercept: $\square$ $y$-intercept: $\square$

Solution

To find the $x$-intercept and $y$-intercept of the line given by the equation $3x + 2y = -12$:

Step 1: Finding the $x$-intercept

To find the $x$-intercept, we set $y = 0$ in the equation $3x + 2y = -12$ and solve for $x$:

\[ 3x + 2(0) = -12 \implies 3x = -12 \implies x = \frac{-12}{3} = -4 \]

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

Step 2: Finding the $y$-intercept

To find the $y$-intercept, we set $x = 0$ in the equation $3x + 2y = -12$ and solve for $y$:

\[ 3(0) + 2y = -12 \implies 2y = -12 \implies y = \frac{-12}{2} = -6 \]

Thus, the $y$-intercept is $-6$.

The $x$-intercept is $\boxed{-4}$ and the $y$-intercept is $\boxed{-6}$.

Was this solution helpful?

Unhelpful

Helpful

Thank you for your feedback.

Copied!