Q25. - Algebra 2

Question

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

$y-x=-9$

Step-by-Step Solution

Answer

The x-intercept of the equation is 9 and y-intercept is $-9$. The graph of the equation $y-x=-9$ is provided below.

Step-1 – Apply the concept of intercepts

The x-intercept of a graph is when the y-coordinate is 0. The point where the graph of the equation cuts the x-axis. 

The y-intercept of a graph is when the x-coordinate is 0. The point where the graph of the equation cuts the y-axis. 

Step-2 –Compute the intercepts

Consider the equation $y-x=-9$. 

To compute the x-intercept, substitute y as 0 in the equation.

$\begin{array}{c}0-x=-9\\ -x=-9\\ x=9\end{array}$

Therefore, the x-intercept is 9. 

Thus, the point at which graph crosses the x-axis is $\left(9,0\right)$.

To compute the y-intercept, substitute x as 0 in the equation.

$\begin{array}{c}y-0=-9\\ y=-9\end{array}$

Therefore, the x-intercept is $-9$. 

Thus, the point at which graph crosses the y-axis is $\left(0,-9\right)$.

Step-3 – Graph the equation

Plot the obtained ordered pairs $\left(9,0\right)$ and $\left(0,-9\right)$ on Cartesian plane to obtain the graph of the equation $y-x=-9$.