Q2. - Algebra 1

Question

Write an equation in slope-intercept form for each graph shown. 

Step-by-Step Solution

Answer

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

Step 1. State the concept of a straight line.

The standard form of slope and intercept form of the straight line is $y=mx+c$.

Here, $m$ is the slope of the straight line and $c$ is the $y$-intercept of the equation.

Also, when both the intercepts are given, use the intercept form of a straight line given below,

$\frac{x}{a}+\frac{y}{b}=1$, where $a$ is the $x$-intercept and $b$ is the $y$-intercept.

Step 2. Substitute the values from the graph.

From the graph, the $x$-intercept $-3$ is while the $y$-intercept is 2.

Write the equation in the intercept form, 

$\frac{x}{-3}+\frac{y}{2}=1$

Step 3. Simplify the equation to get slope-intercept form.

Convert this equation in slope and intercept form by separating the $y$ from the equation in the intercept form.

$-\frac{x}{3}+\frac{y}{2}=1$

             $$\begin{gathered} y=2\left(1+\frac{x}{3}\right) \\ y=2+\frac{2}{3}x \\ y=\frac{2}{3}x+2 \end{gathered}$$

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

Therefore, the equation of the straight line is $y=\frac{2}{3}x+2$.