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=(24)/(6) \\ \\ x=4 \end{gathered}`

x-intercept is

`(4,0)`

y-intercept

`\begin{gathered} 6(0)+12y=24 \\ 12y=24 \\ y=(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=(-24)/(-5) \\ \\ x=(24)/(5) \end{gathered}`

x-intercept is

`((24)/(5),0)`

Y-intercept

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

y-intercept is

`(0,-8)`