Q12. - Algebra 1

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

Step-by-Step Solution

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 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 2 3 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 = 2 3 x + 3 .

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