Q1. - 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 $\mathit{y}\mathbf{=}\frac{\mathbf{14}}{\mathbf{5}}\mathit{x}\mathbf{+}\mathbf{7}$.

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 $-2.5$ is while the $y$-intercept is 7.

Write the equation in the intercept form, 

 $\frac{x}{-2.5}+\frac{y}{7}=1$

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.

  $$\begin{gathered} \frac{x}{-2.5}+\frac{y}{7}=1 \\ -\frac{2}{5}x+\frac{y}{7}=1 \\ y=7\left(1+\frac{2}{5}x\right) \\ y=7+\frac{14}{5}x \\ y=\frac{14}{5}x+7 \end{gathered}$$ 

The equation of the straight line in the slope and intercept form is $y=\frac{14}{5}x+7$.

Therefore, the equation of the straight line is $y=\frac{14}{5}x+7$.