Question

Find the \(x\) -intercept and the \(y\) -intercept of the graph of the equation. $$3 y=6 x+3$$

Short answer

The x-intercept of the graph of the equation is \(-\frac{1}{2}\), and the y-intercept is 1.

Step-by-step solution

Find the x-intercept

To find the x-intercept of the equation, substitute y = 0. into the given equation. This gives \(3(0)=6x+3 \Rightarrow 6x+3=0 \Rightarrow x=-\frac{3}{6}=-\frac{1}{2}\).

Find the y-intercept

To find the y-intercept of the equation, substitute x = 0. into the given equation. This gives \(3y=6(0)+3 \Rightarrow 3y=3 \Rightarrow y=1.\)