how to write an equation for the linear function f with the given values.

Question

f (0)=21,f (4)=13

Answer 1

y = f(x) so basically you're given two points: P₁(0,21) and P₂(4,13). From these two points we can determine the equation of a line through both points.The general equation is y=mx+b where m = slope and b= y-intercept.

The slope m = (y₂-y₁)/(x₂-x₁) = (13-21)/(4-0) = -8/4 = -2 (it doesn't matter which one is point 1 or point 2 really. We could have easily done (21-13)/(0-4)=8/-4 = -2).

Now that we have the slope, we can write y = -2x + b. Since we have an x and a y from one of the points (any one, doesn't matter) we can find our y-intercept, b. Using P₁(0,21) we get 21 = -2(0) + b, or b=21. (if we used P₂(4,13) instead, we get 13 = -2(4) + b ⇒ 21 = b.

Now that we have our slope m and y-intercept b we can write the general form of the equation, y = -2x + 21.