Q10. - 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: 3, $y$-intercept: 5

Step-by-Step Solution

Answer

The equation in slope-intercept form is  and the graph of the equation is:

Step 1. State the concept of the 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 the equation of a line in slope-intercept form.

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

The equation of the straight line is:

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

Step 3. Graph the equation.

To graph the equation, plot the $y$-intercept $\left(0,5\right)$. The slope is $\frac{\text{rise}}{\text{run}}=\frac{3}{1}$. From $\left(0,5\right)$, move up 5 units and right 1 unit. Plot the point. Draw the line through the two points. 

 

Therefore, the equation of the straight line is $y=3x+5$ and the graph of the equation is drawn above.