Question

find the x- and y-intercepts of the graphs of each equation6x+12y=24-5x+3y=-24

Answer 1

To find the x-intercept we replace y=0 and solve for x

To find the y-intercept we repalce x=0 and solve for y

First equation

$6x+12y=24$

x-intercept

$\begin{gathered} 6x+12(0)=24 \\ 6x=24 \\ x=\frac{24}{6} \\ \\ x=4 \end{gathered}$

x-intercept is

$(4,0)$

y-intercept

$\begin{gathered} 6(0)+12y=24 \\ 12y=24 \\ y=\frac{24}{12} \\ \\ y=2 \end{gathered}$

y-intercept is

$(0,2)$

Second equation

$-5x+3y=-24$

x-intercept

$\begin{gathered} -5x+3(0)=-24 \\ -5x=-24 \\ x=\frac{-24}{-5} \\ \\ x=\frac{24}{5} \end{gathered}$

x-intercept is

$(\frac{24}{5},0)$

Y-intercept

$\begin{gathered} -5(0)+3y=-24 \\ 3y=-24 \\ y=\frac{-24}{3} \\ \\ y=-8 \end{gathered}$

y-intercept is

$(0,-8)$