Answer:
![y=-5x+2](https://tex.z-dn.net/?f=y%3D-5x%2B2)
Step-by-step explanation:
Hi there!
<u>What we need to know:</u>
- Slope-intercept form:
where m is the slope and b is the y-intercept (the value of y when x is 0)
<u>1) Determine the slope (m)</u>
<u />
where two points that the line passes through are
and ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
Plug in the given points (1,-3) and (-3,17)
![=\frac{17-(-3)}{-3-1}\\=\frac{17+3}{-3-1}\\=\frac{20}{-4}\\=-5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B17-%28-3%29%7D%7B-3-1%7D%5C%5C%3D%5Cfrac%7B17%2B3%7D%7B-3-1%7D%5C%5C%3D%5Cfrac%7B20%7D%7B-4%7D%5C%5C%3D-5)
Therefore the slope of the line is -5. Plug this into
:
![y=-5x+b](https://tex.z-dn.net/?f=y%3D-5x%2Bb)
<u>2) Determine the y-intercept (b)</u>
![y=-5x+b](https://tex.z-dn.net/?f=y%3D-5x%2Bb)
Plug in one of the given points and solve for b
![-3=-5(1)+b\\-3=-5+b](https://tex.z-dn.net/?f=-3%3D-5%281%29%2Bb%5C%5C-3%3D-5%2Bb)
Add 5 to both sides of the equation to isolate b
![-3+5=-5+b+5\\2=b](https://tex.z-dn.net/?f=-3%2B5%3D-5%2Bb%2B5%5C%5C2%3Db)
Therefore, the y-intercept of the equation is 2. Plug this back into
:
![y=-5x+2](https://tex.z-dn.net/?f=y%3D-5x%2B2)
I hope this helps!