Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

Answer:

$y=-\frac{1}{4} x-6$

Step-by-step explanation:

The slope-intercept form is $y=mx+c$, where m is the slope of the line and c is where the line crosses the $y$-axis.

To calculate $m$ we can use the formula $m = \frac{dy}{dx}$ where $dy$ is the difference in $y$ between two points and $dx$ is the difference between $x$.

Information we can get from the graph given: $c=-6$. Since $c$ is the point at which the line crosses the $y$-axis.

To find $m$ let's get two points from the graph.

Point 1: $(4,-7)$

Point 2: $(8,-8)$

Now use the equation $m = \frac{dy}{dx}$.

$m = \frac{-7 - (-8)}{4-8} = -\frac{1}{4}$.

Now we have $m$ and $c$, let's put them back into the general equation.

$y=-\frac{1}{4} x-6$