Question

Find the \(x\) -intercept and the \(y\) -intercept of the graph of the equation. $$y=2 x+12$$

Short answer

The x-intercept of the graph is \(-6, 0\) and the y-intercept is \(0, 12\).

Step-by-step solution

Find the x-intercept

Set \(y = 0\) in the equation and solve for \(x\). Doing this gives us: \(0=2x + 12\).

Solve for x

Solve the equation \(0=2x + 12\) by subtracting 12 from both sides to get \(2x = -12\). Then, divide by 2, yielding \(x = -6\). Therefore, the coordinate of the x-intercept is \(-6, 0\).

Find the y-intercept

The y-intercept is where \(x = 0\). Substitute \(x = 0\) into the equation to get \(y = 2(0) + 12\).

Solve for y

Solving the equation \(y = 2(0) + 12\), gives \(y = 12\). Therefore, the coordinate of the y-intercept is \(0, 12\).