Problem 14 - Algebra 1: Concepts and Skills

Question

Find the \(x\) -intercept and the \(y\) -intercept of the graph of the equation. Graph the equation. $$ x-y=1 $$

Step-by-Step Solution

Answer

The x-intercept is 1 and the y-intercept is -1. The graph is a straight line passing through these intercepts on the Cartesian plane.

Step 1: Find the X-intercept

To find the x-intercept, you set \(y = 0\) in the given equation. The equation becomes \(x - 0 = 1\), therefore, \(x = 1\). So the x-intercept is 1.

Step 2: Find the Y-intercept

To find the y-intercept, set \(x = 0\) in the given equation. The equation becomes \(0 - y = 1\), which simplifies to \(-y = 1\). Solving for \(y\), we get \(y = -1\). Therefore, the y-intercept is -1.

Step 3: Graphing the equation

Plot the x-intercept 1 and the y-intercept -1 on the Cartesian plane. Join these points with a line as the equation is linear, which results in a straight line. That line is the graphical representation of the equation \(x - y = 1\).