Q4. - Algebra 1

Question

Write an equation of a line in slope-intercept form with the given slope and $\mathit{y}$-intercept. Then graph the equation.

Slope: $\mathbf{-}\frac{\mathbf{5}}{\mathbf{7}}$, y-intercept: $\mathbf{-}\frac{\mathbf{2}}{\mathbf{3}}$

Step-by-Step Solution

Answer

The equation in slope-intercept form is $\mathit{y}\mathbf{=}\mathbf{-}\frac{\mathbf{5}}{\mathbf{7}}\mathit{x}\mathbf{-}\frac{\mathbf{2}}{\mathbf{3}}$ and the graph of the equation is:

Step 1. State the concept of standard form 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.

To find the equation of a line in slope-intercept form substitute $-\frac{5}{7}$ for $m$  and $-\frac{2}{3}$ for b in the equation $y=mx+b$.

The equation of the straight line is:

 $\begin{array}{l}y=mx+b\\ y=-\frac{5}{7}x-\frac{2}{3}\end{array}$

Step 3. Graph the equation.

Plot this equation on the Cartesian plane.

Therefore, the equation of the straight line is $y=-\frac{5}{7}x-\frac{2}{3}$ and the graph of the equation is drawn above.