Q7. - Algebra 1

Question

Graph each equation.

 $\mathbf{-}\mathbf{3}\mathit{x}\mathbf{+}\mathbf{7}\mathit{y}\mathbf{=}\mathbf{21}$

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 equation of a line in slope-intercept form.

Rewrite the equation $-3x+7y=21$ in slope-intercept form.

The equation of the straight line is:

$\begin{array}{l}-3x+7y=21\\ -3x+7y+3x=21+3x\text{ Add }3x\text{ both sides}\\ \frac{7y}{7}=\frac{3x+21}{7}\text{ Divide both sides by }7\\ y=\frac{3}{7}x+3\end{array}$

The slope is $m=\frac{3}{7}$ and the $y$-intercept is $(0,3)$.

Step 3. Graph the equation.

To graph the equation, plot the $y$-intercept $(0,3)$. The slope is $\frac{\text{rise}}{\text{run}}=\frac{3}{7}$. From $(0,3)$, move up 3 units and right 7 units. Plot the point. Draw the line through the two points.