Precalculus math

Question

If  is a linear function, , and , find an equation for 

 =

Answer 1

(-4,5) and (3,0) are two points on the line. (3,0) is the line's x intercept

the slope = (5-0)/(-4-3) = 5/(-7) = -5/7 = "rise over run"

f(x) = y= mx + b were m= slope and b = y intercept

y=-5x/7 + b, solve for b by plugging in either point

0=-5(3)/7 + b

b= 15/7

y=-5x/7 + 15/7

f(x) = -5x/7 +15/7

Answer 2

A linear function can be written as y = mx + b or, f(x) = mx + b. To find the complete function, we need to determine what the values of "m" and "b" are.

We can use the two points that were given (both in the form of (x, y) as values to find the "m" and "b". To do so, plug them in as "x" and "y" values like this:

y = mx + b

1) 5 = m(-4) + b or -4m + b = 5

2) 0 = m(3) + b or 3m + b = 0

Using equation 2) we can subtract 3m from both sides to get b = -3m then we can plug "-3m" into equation 1) wherever we see "b" because "b" and "-3m" are the same (they are equal). So:

-4m + (-3m) = 5

-7m = 5

m = -5/7

Plugging m = -5/7 into equation 2, we get:

3(-5/7) + b = 0

-15/7 + b = 0

b = 15/7

So the function is:

y = -5/7x + 15/7

or, written in function notation: f(x) = -5/7x + 15/7

Answer 3