Q2B. - Algebra 1

Question

Graph each equation.

$-2x+5y=10$

Step-by-Step Solution

Answer

The graph of the equation is:

Step 1. State the concept of slope-intercept of an equation.

The slope-intercept form of a linear equation is $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept.

Step 2. Write the equation of a line in slope-intercept form.

Rewrite the equation $-2x+5y=10$ in slope-intercept form.

The equation of the straight line is:

$$\begin{gathered} -2x+5y=10 \\ -2x+5y+2x=10+2x\text{ Add 2}x\text{ both sides} \\ \frac{5y}{5}=\frac{10+2x}{5}\text{ Divide both sides by }5 \\ y=\frac{2}{5}x+2 \end{gathered}$$

The slope is $m=\frac{2}{5}$ and the $y$-intercept is $\left(0,2\right)$.

Step 3. Graph the equation.

To graph the equation, plot the $y$-intercept $\left(0,2\right)$. The slope is $\frac{\text{rise}}{\text{run}}=\frac{2}{5}$. From $\left(0,2\right)$, move up 2 units and right 5 units. Plot the point. Draw the line through the two points.