SOLUTION: What is the linear function f with the given values? F( -4) = -2, f(2) = 7

Question 822876: What is the linear function f with the given values?
F( -4) = -2, f(2) = 7
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
F( -4) = -2, f(2) = 7 means we have the two points on the line: (-4,-2) and (2,7)

First let's find the slope of the line through the points

and

Note:

is the first point

. So this means that and .
Also,

is the second point

. So this means that and .

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

Reduce

So the slope of the line that goes through the points

and

is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Rewrite as

Rewrite as

Distribute

Multiply

Subtract 2 from both sides.

Combine like terms.

So the equation that goes through the points

and

is

Therefore, the function is
RELATED QUESTIONS
What is the equation for the linear function f with the given values? F(-4) = 5, f(2)... (answered by TimothyLamb)

F(-10)=4, F(-2)=4 Write a linear function F with the given... (answered by ikleyn)

Write a linear function f with the values f(2)=4 and... (answered by josmiceli)

What is a linear equation for f in the given:... (answered by richwmiller)

Write a linear function f with the values f(0)=2 and... (answered by Boreal)

how do you write an equation for a linear function f with the given values the problem i (answered by ReadingBoosters)

Find f(3), given that f is a linear function with f(1)=2 and... (answered by rothauserc)

write an equation for the linear function f satisfying the given conditions 1. f(3)=4... (answered by Edwin McCravy)

The table shows values for a linear function, f(x). x f(x) -1 -8 3 -5 7 (answered by Boreal)