Question

Write a rule for the linear function in each table.

Answer 1

Answer:

Part 1) $f(x)=4x+3$

Part 2) $f(x)=2x+1$

Part 3) $f(x)=x-4$

Step-by-step explanation:

Table 1

step 1

Find the slope

take two points from the data in the table

(0,3) and (3,15)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{15-3}{3-0}$

$m=\frac{12}{3}=4$

step 2

Find the linear function in slope intercept form

$f(x)=mx+b$

we have

$m=4\\b=3$

substitute

$f(x)=4x+3$

Table 2

step 1

Find the slope

take two points from the data in the table

(2,5) and (5,11)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{11-5}{5-2}$

$m=\frac{6}{3}=2$

step 2

Find the linear function in slope intercept form

$f(x)=mx+b$

we have

$m=2\\point\ (2,5)$

Solve for b

substitute

$5=2(2)+b\\b=5-4\\b=1$

therefore

$f(x)=2x+1$

Table 3

step 1

Find the slope

take two points from the data in the table

(5,1) and (8,4)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{4-1}{8-5}$

$m=\frac{3}{3}=1$

step 2

Find the linear function in slope intercept form

$f(x)=mx+b$

we have

$m=1\\point\ (5,1)$

Solve for b

substitute

$1=1(5)+b\\b=1-5\\b=-4$

therefore

$f(x)=x-4$