Question

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

Answer 1

hello

the equation given is

$\frac{1}{2}x+\frac{1}{4}y=\frac{3}{2}$

let's rewrite the equation

$\begin{gathered} \frac{1}{2}x+\frac{1}{4}y=\frac{3}{2} \\ \frac{1}{4}y=\frac{3}{2}-\frac{1}{2}x \\ \text{ multiply through by 4} \\ \frac{4}{4}y=4\times\frac{3}{2}-(4\times\frac{1}{2}x) \\ y=\frac{12}{2}-2x \\ y=6-2x \end{gathered}$

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

$\begin{gathered} y=6-2x \\ 0=6-2x \\ 2x=6 \\ \text{divide both sides by 2} \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}$

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