Problem 13 - Algebra 1: Concepts and Skills

Question

Find the \(x\) -intercept and the \(y\) -intercept of the graph of the equation. Graph the equation. $$ 5 y=5 x+15 $$

Step-by-Step Solution

Answer

The x-intercept of the equation is -3 and the y-intercept is 3. The graph of the equation is a straight line passing through the points (-3,0) and (0,3).

Step 1: Rewrite the Equation

The equation should be rearranged to 'y=mx+b' form. Divide every term in the equation \(5y=5x+15\) by 5. \(y=x+3\) is the result.

Step 2: Find the x-intercept

The x-intercept is the x-coordinate where the graph intersects the x-axis. That happens when y=0. We substitute y=0 in the equation and solve for x. So, when y=0, \(0=x+3\). Solving for x, x=-3 is the x-intercept.

Step 3: Find the y-intercept

The y-intercept is the y-coordinate where the graph intersects the y-axis. That happens when x=0. We substitute x=0 in the equation and solve for y. So, when x=0, \(y=0+3\). Therefore, y=3 is the y-intercept.

Step 4: Graph the Equation using the Intercept

To graph the equation, plot the x-intercept (-3,0) and the y-intercept (0,3) on the graph. Then draw a straight line through these points. This line represents the graph of the equation \(y=x+3\).