Respuesta :

absor201

Answer:

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

Step-by-step 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

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