Question

Find the x-intercept and the y-intercept of the graph of the equation. $$y=x-5$$

Short answer

The x-intercept of the graph of the equation is 5 and the y-intercept is -5. In terms of points, the x-intercept is at the point (5,0) and the y-intercept is at the point (0,-5).

Step-by-step solution

Find the x-intercept

To find the x-intercept, set \(y=0\) and solve the equation for \(x\). In the given equation, when substituting \(y=0\), we get \(0=x-5\). Solving for \(x\) gives \(x=5\). So, the x-intercept is 5.

Find the y-intercept

To find the y-intercept, set \(x=0\) and solve the equation for \(y\). In the given equation, when substituting \(x=0\), we get \(y=0-5\). Solving for \(y\) gives \(y=-5\). So, the y-intercept is -5.

State the Intercept Points

From step 1 and step 2, \(x\)-intercept is at the point (5,0) and \(y\)-intercept is at the point (0,-5).