Question

Find an equation for the family of linear functions such that f(4) = 1.

Answer 1

Answer: 1 = 4m + b

Step-by-step explanation

The template of a linear equation is y = mx+b, where,

• m = slope
• b = y intercept

This is known as slope-intercept form.

We're told that f(4) = 1. It means (x,y) = (4,1). The input x = 4 leads to the output y = f(x) = 1.

y = mx + b

1 = m*4 + b

1 = 4m + b

That equation describes a family of linear functions that pass through (4,1)

There are infinitely many possibilities to replace m and b with. Once a value of m is chosen, then b is locked into place, and vice versa.

For instance, if m = 0, then b = 1. Another example: if m = 1 then b = -3.