SOLUTION: Find the equation of the linear function which passes through the points (0,5) and (-3, 20)

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the linear function which passes through the points (0,5) and (-3, 20)      Log On


   

Question 302337: Find the equation of the linear function which passes through the points (0,5) and (-3, 20)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=0 and y%5B1%5D=5.
Also, is the second point . So this means that x%5B2%5D=-3 and y%5B2%5D=20.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%2820-5%29%2F%28-3-0%29 Plug in y%5B2%5D=20, y%5B1%5D=5, x%5B2%5D=-3, and x%5B1%5D=0


m=%2815%29%2F%28-3-0%29 Subtract 5 from 20 to get 15


m=%2815%29%2F%28-3%29 Subtract 0 from -3 to get -3


m=-5 Reduce


So the slope of the line that goes through the points and is m=-5


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-5=-5%28x-0%29 Plug in m=-5, x%5B1%5D=0, and y%5B1%5D=5


y-5=-5x%2B5%280%29 Distribute


y-5=-5x%2B0 Multiply


y=-5x%2B0%2B5 Add 5 to both sides.


y=-5x%2B5 Combine like terms.



So the equation that goes through the points and is y=-5x%2B5