Can you write an equation for a line with 𝑓(0)=2 and 𝑓(3)=−4 and use it to find 𝑓(−5).?

Question

Lesson 5.1A: Writing Equations in Slope Intercept Form

Answer 1

Slope intercept form: y = mx + b

m is the slope which we need to calculate

b is the y intercept, also known as the y value when x = 0

f(x) = y can also be written as x,y

therefore f(0) = 2 is the same as (0,2) and f(3) = -4 is the same as (3,-4)

Now we take the difference between the y values over the x values to calculate the slope:

Slope= m = (y2 - y1) / (x2 - x1)

m = (-4 -2) / (3 - 0)

m = -6 / 3

m = -2

the y intercept, or the value of b, is essentially given, the point (0,2) so b = 2

we now have all the information we need:

y = mx + b

y = -2x + 2

To double check we can put in the first 2 values we were given:

when x = 0 or f(0):

y = -2(0) + 2

y = 2

and when x = 3 or f(3):

y = -2(3) + 2

y = -6 + 2

y = -4

both gave us the same answers as given so we know this is the right function, all we have to do now is plug in the new x value

when x = -5 or f(-5):

y = -2(-5) + 2

y = 10 + 2

y = 12

therefore f(-5) = 12