Answer:
If only slope:
[tex]y = \frac{4}{5}x + b[/tex]
If slope and y-intercept:
[tex]y = \frac{4}{5}x - 6.6\\or\\y = \frac{4}{5}x - 3.4[/tex]
*both are correct answers see steps below*
Step-by-step explanation:
The equation to find the slope is [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].
The equation for slope-intercept form is [tex]y = mx + b[/tex].
First, find the slope between two points.
[tex]\frac{-1 - (-5)}{3 - (-2)} = \frac{4}{5}[/tex]
Keep the difference as a fraction if it can't be divided.
Next, plug in the slope value into the equation.
[tex]y = \frac{4}{5}x + b[/tex]
If you also need to find what b is, pick a point; (-2, -5) OR (3, -1). Then fill in the equation with it's x and y values. (I'll do both points to show two different results).
Point (-2, -5):
[tex](-5) = \frac{4}{5}(-2) + b[/tex]
[tex](-5) = (-1.6) + b[/tex]
Add 1.6 on both sides to isolate the b. (since -1.6 is a negative, we need to cancel it out with its opposite)
[tex]b = -6.6[/tex]
Point (3, -1):
[tex](-1) = \frac{4}{5}(3) + b[/tex]
[tex](-1) = (2.4) + b[/tex]
Subtract 2.4 on both sides to isolate the b. (since 2.4 is a positive, we need to cancel it out with its opposite)
[tex]b = -3.4[/tex]
It does mean that both slopes have different y-intercepts but it overly depends on the point. These steps will ensure you to the correct answer.
