Question

Find the \(x\) -intercept and the \(y\) -intercept of the graph of the equation. $$y=3 x+9$$

Short answer

The \(x\)-intercept is -3 and the \(y\)-intercept is 9.

Step-by-step solution

Identify the y-intercept

We can directly obtain the \(y\)-intercept from the equation. It is the constant term \(c\) in the equation \(y = mx + c\). So, in our equation \(y = 3x + 9\), the \(y\)-intercept is 9.

Find the x-intercept

The \(x\)-intercept is the value of \(x\) when \(y = 0\). We can find it by substituting \(y = 0\) in the given equation and solving for \(x\):\[\begin{{align*}}0 &= 3x + 9 \3x &= -9 \x &= -3 .\end{{align*}}\]So, the \(x\)-intercept is -3.