I do not understand what to do

Question

Write a linear function with f (-4)=2 and f (6)=-3

Answer 1

Aspen, maybe you need help understanding the function notation.

to say that f(-4) = 2 means that when x = -4, y = 2.

It could be said that the point (-4, 2) is on the line.

With that out of the way, we could re-phrase the question such as:

Write the equation for the line connecting the points (-4, 2) and (6, -3)

To answer this question, we begin by finding the slope using the slope formula. (The ratio of rise over run)

m = (-3 - 2)/(6 - (-4)) = -5/10 = -1/2

Next, we can pick one of the points and plug numbers into the point-slope form.

The point-slope form looks like this; y - y₁ = m(x - x₁) where m is the slope and (x₁, y₁) is a known point.

I'll use (-4, 2) to get.

y - 2 = -1/2(x - (- 4)) or because of the double negative, let's change this to y - 2 = -1/2(x + 4).

We're done because the question didn't specify a form.

But let's go further. Suppose we were asked to express our answer in the slope-intercept form.

That form appears as y = mx +b.

We need to distribute the -1/2 through the parenthesis and add 2 to solve for y.

y = -1/2x - 2 + 2. The 2's cancel and we get y = -1/2x.

I hope this helps.

Answer 2

(-4,2) and (6,-3) are points on the line

Slope = (-3-2) / (6-(-4)) = -1/2

Equation of line is y - 2 = (-1/2)(x - (-4))

y - 2 = (-1/2)x - 2

y = f(x) = (-1/2)x