Problem 9 - Algebra 1: Concepts and Skills

Question

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

Step-by-Step Solution

Answer

The \(x\)-intercept is -2 and the \(y\)-intercept is 2.

Step 1: Finding the \(x\)-intercept

To find the \(x\)-intercept, set \(y=0\) in the equation and solve for \(x\). Plugging \(y=0\) into the equation \(y=x+2\), we get \(0=x+2\). Solving for \(x\) gives \(x=-2\). So the \(x\)-intercept is -2.

Step 2: Finding the \(y\)-intercept

To find the \(y\)-intercept, set \(x=0\) in the equation and solve for \(y\). Plugging \(x=0\) into the equation \(y=x+2\), we get \(y=0+2\). Simplifying this gives \(y=2\). So the \(y\)-intercept is 2.

Step 3: Graphing the equation

To graph the equation \(y=x+2\), we can use the intercepts found in previous steps. We plot the \(x\)-intercept at (-2, 0) and the \(y\)-intercept at (0, 2), then draw a straight line through these two points. These two points are enough to define the line since it is a linear equation.