Q9. - Algebra 2

Question

Find the $x$-intercept and the $y$-intercept of the graph of each equation. Then graph the equation.

 

$y=-3x-5$

Step-by-Step Solution

Answer

The x-intercept is $-\frac{5}{3}$ and y-intercept is -5. The graph of the equation is:

Step 1 – Definition of intercepts.

The x-intercept is the point where the graph intersect the x-axis. It is the value of x when y=0.

The y-intercept is the point where the graph intersect the y-axis. It is the value of y when $x=0$.

Step 2 – Find the x -intercept.

The given equation is:

$y=-3x-5$

Substitute y=0 in the given equation.

$\begin{array}{c}0=-3x-5\\ 3x=-5\\ \frac{3x}{3}=-\frac{5}{3}\\ x=-\frac{5}{3}\end{array}$

The x-intercept is $-\frac{5}{3}$. The graph crosses the x-axis at $\left(-\frac{5}{3},0\right)$.

Step 3 – Find the y -intercept.

Substitute x=0 in the given equation.

$\begin{array}{c}y=-3\left(0\right)-5\\ y=0-5\\ y=-5\end{array}$

The y-intercept is -5. The graph crosses the y-axis at $\left(0,-5\right)$.

Step 4 – Draw the graph.

 Plot the points $\left(-\frac{5}{3},0\right)$ and $\left(0,-5\right)$ on a coordinate plane and connect them by a straight line as shown below:

Thus, the x-intercept is $-\frac{5}{3}$ and y-intercept is -5.