Question

Write a linear function $f$ with the values $f(0)=8$ and $\ f(4)=20$ .

Answer 1

f(x) = 3x + 8 is the required linear function.

Explanation:

We know that the slope-intercept form of linear equation is

y = mx+b

here

• m is the slope of the line, and

• b is the y-intercept

Given initial value

f(0) = 8

• Meaning at x = 0, y = 8

Thus, the y-intercept = b = 8

Also given

at x = 4, f(4) = 20

• Meaning at x=4, y = 20

so

substituting the point (4, 20) and y-intercept b=8 in the slope-intercept form to determine the slope

y = mx+b

20 = m(4) + 8

20 = 4m + 8

4m = 20-8

4m = 12

Dividing both sides by 4

m = 3

Thus, the slope = m = 3

Now, substituting m = 3 and b = 8 in the slope-intercept of linear function

y = mx+b

y = 3x + 8

or

f(x) = 3x + 8

Thus,

f(x) = 3x + 8 is the required linear function.

VERIFICATION:

Given the linear function

f(x) = 3x + 8

plug in x = 0

f(0) = 3(0) + 8

f(0) = 8

plug in x = 4

f(x) = 3x + 8

f(4) = 3(4) + 8

f(4) = 12+8

f(4) = 20