Q.3.19 - Intermediate Algebra

Question

Graph using the intercepts:

$5x-2y=10$

Step-by-Step Solution

Answer

The graph of the equation is

Step 1. Given Information

Given equation is $5x-2y=10$

The graph of the equation is to be determined using the intercepts.

Step 2. Find the x-intercept

To determine the x-intercept, plugging $y=0$ in the equation and solving for x:

$$\begin{gathered} 5x-2y=10 \\ 5x-2\left(0\right)=10 \\ 5x-0=10 \\ 5x=10 \\ \frac{5x}{5}=\frac{10}{5} \\ x=2 \end{gathered}$$

So the x-intercept is $\left(2,0\right)$

Step 3. Find the y-intercept

To determine the y-intercept, plugging $x=0$ in the equation and solving for y:

$$\begin{gathered} 5x-2y=10 \\ 5\left(0\right)-2y=10 \\ 0-2y=10 \\ -2y=10 \\ \frac{-2y}{-2}=\frac{10}{-2} \\ y=-5 \end{gathered}$$

So the y-intercept is $\left(0,-5\right)$

Step 4. Plotting the intercepts

Plotting the intercepts on the coordinate plane and joining them using a line:

Step 5. Conclusion

The graph of the equation using the intercepts is