Question

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

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

Short answer

The equation of a line in slope-intercept form with the given slope and $y$-intercept is $y=\frac{2}{3}x+3$.

The graph of the equation$y=\frac{2}{3}x+3$is:

Step-by-step solution

Step 1. Write the slope-intercept form of a line.

The equation of line in slope-intercept form is:

$y=mx+b$

Where$m$ is the slope of the line and$b$ is the $y$-intercept of the line.

Step 2. Write the equation of a line in slope-intercept form having slope 23 and y-intercept 3.

The slope of the line is $\frac{2}{3}$. Therefore, the value of$m$ is $\frac{2}{3}$.

The $y$-intercept of the line is 3. Therefore, the value of$b$ is 3.

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

$$\begin{gathered} y=mx+b \\ =\left(\frac{2}{3}\right)x+\left(3\right) \\ =\frac{2}{3}x+3 \end{gathered}$$

Therefore, the equation of a line in slope-intercept form with the given slope and $y$-intercept is $y=\frac{2}{3}x+3$.

Step 3. Draw the graph of the equation y=23x+3.

The graph of the equation $y=\frac{2}{3}x+3$is: