Questions: Find the x-intercept and y-intercept of the line. 4 x+6 y=-24

Transcript text: Find the $x$-intercept and $y$-intercept of the line. \[ 4 x+6 y=-24 \]

Solution

Solution Steps

To find the $x$-intercept and $y$-intercept of the line given by the equation $4x + 6y = -24$:

Finding the $x$-intercept: Set $y = 0$ in the equation and solve for $x$.
Finding the $y$-intercept: Set $x = 0$ in the equation and solve for $y$.

Step 1: Finding the $ x $-intercept

To find the $ x $-intercept, we set $ y = 0 $ in the equation $ 4x + 6y = -24 $: \[ 4x + 6(0) = -24 \implies 4x = -24 \implies x = -6 \] Thus, the $ x $-intercept is $ -6 $.

Step 2: Finding the $ y $-intercept

To find the $ y $-intercept, we set $ x = 0 $ in the equation $ 4x + 6y = -24 $: \[ 4(0) + 6y = -24 \implies 6y = -24 \implies y = -4 \] Thus, the $ y $-intercept is $ -4 $.