SOLUTION: write an equation for the linear function f with the given values. f(0)=-1, f(3)=-10

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Question 236025: write an equation for the linear function f with the given values.
f(0)=-1, f(3)=-10
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since f(0)=-1, f(3)=-10 this means we have the two points (0,-1) and (3,-10)



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=-1.
Also, is the second point . So this means that x%5B2%5D=3 and y%5B2%5D=-10.


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


m=%28-10--1%29%2F%283-0%29 Plug in y%5B2%5D=-10, y%5B1%5D=-1, x%5B2%5D=3, and x%5B1%5D=0


m=%28-9%29%2F%283-0%29 Subtract -1 from -10 to get -9


m=%28-9%29%2F%283%29 Subtract 0 from 3 to get 3


m=-3 Reduce


So the slope of the line that goes through the points and is m=-3


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--1=-3%28x-0%29 Plug in m=-3, x%5B1%5D=0, and y%5B1%5D=-1


y%2B1=-3%28x-0%29 Rewrite y--1 as y%2B1


y%2B1=-3x%2B-3%28-0%29 Distribute


y%2B1=-3x%2B0 Multiply


y=-3x%2B0-1 Subtract 1 from both sides.


y=-3x-1 Combine like terms.


y=-3x-1 Simplify


So the equation that goes through the points and is y=-3x-1


Notice how the graph of y=-3x-1 goes through the points and . So this visually verifies our answer.
Graph of y=-3x-1 through the points and