Q1A. - 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: $-\frac{1}{2}$, $y$-intercept: 3

Step-by-Step Solution

Answer

The equation in slope-intercept form is $y=-\frac{1}{2}x+3$ 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 $-\frac{1}{2}$ for $m$ and 3 for $b$ in the equation $y=mx+b$.

The equation of the straight line is:

 $$\begin{gathered} y=mx+b \\ y=-\frac{1}{2}x+3 \end{gathered}$$

 

Step 3. Graph the equation.

To graph the equation, plot the $y$-intercept $\left(0,3\right)$. The slope is $\frac{\text{rise}}{\text{run}}=-\frac{1}{2}$. From $\left(0,3\right)$, move down 1 unit and right 2 units. Plot the point. Draw the line through the two points.  

 

Therefore, the equation of the straight line is $y=-\frac{1}{2}x+3$ and the graph of the equation is drawn above.