Question

Find the x- and y- intercept of each linear equation.1/2x + 1/4y = 3/2

Answer 1

hello

the equation given is

`(1)/(2)x+(1)/(4)y=(3)/(2)`

let's rewrite the equation

`\begin{gathered} (1)/(2)x+(1)/(4)y=(3)/(2) \\ (1)/(4)y=(3)/(2)-(1)/(2)x \\ \text{ multiply through by 4} \\ (4)/(4)y=4*(3)/(2)-(4*(1)/(2)x) \\ y=(12)/(2)-2x \\ y=6-2x \end{gathered}`

now let's find the x and y intercept now

to do this, put x = 0 and solve and then put y = 0 and then solve

`\begin{gathered} y=6-2x \\ \text{put x = 0} \\ y=6-2(0) \\ y=6-0 \\ y=6 \end{gathered}`

now let's put y = 0

`\begin{gathered} y=6-2x \\ 0=6-2x \\ 2x=6 \\ \text{divide both sides by 2} \\ (2x)/(2)=(6)/(2) \\ x=3 \end{gathered}`

now the coordinates for the equation is (3, 6)