Question

Graph each equation using the x- and y-intercepts.

$2x+5y=10$

Short answer

The graph by using the x and y intercepts is:

Step-by-step solution

Step 1. State the concept for plotting a straight-line using equation.

The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis.

Then, algebraically,

• an x-intercept is a point on the graph where y is zero, and
• a y-intercept is a point on the graph where x is zero.

More specifically,

• an x-intercept is a point in the equation where the y-value is zero, and
• a y-intercept is a point in the equation where the x-value is zero.

Step 2. Calculate the x and y-intercepts.

To find the x-intercept, plug in $y=0$in the equation $2x+5y=10$ and solve for x.

$$\begin{gathered} 2x+5y=10 \\ 2x+5\cdot 0=10[\text{Plug\hspace{0.17em}\hspace{0.17em}in\hspace{0.17em}\hspace{0.17em}}y=0] \\ 2x+0=10 \\ 2x=10 \\ \frac{2x}{2}=\frac{10}{2} \\ x=5 \end{gathered}$$

Therefore, x-intercept is $x=5$.

Now to find the y-intercept, plug in $x=0$ in the equation$2x+5y=10$ and solve for y.

$$\begin{gathered} 2x+5y=10 \\ 2\cdot 0+5y=10[\text{Plug\hspace{0.17em}\hspace{0.17em}in\hspace{0.17em}\hspace{0.17em}}x=0] \\ 0+5y=10 \\ 5y=10 \\ \frac{5y}{5}=\frac{10}{5} \\ y=2 \end{gathered}$$

Therefore, y-Intercept is $y=2$.

Step 3. Plot the graph.

Graph the line$2x+5y=10$ with x and y intercepts points are $\left(5,0\right)$and $\left(0,\text{2}\right)$.