Question

7. Use the data in each table to write a linear function using function notation​

Answer 1

Answer:

Answer

Step-by-step explanation:

7. f(x)=0.2x

8. f(x)=3x+5

9. f(x)=-2x-2

Answer 2

According to the tables, the linear functions are given by:

• 7. $y = 0.2x$.

• 8. $y = 3x + 5$.

• 9. $y = -2x - 2$.

Linear function:

A linear function is modeled by:

$y = mx + b$

In which:

• m is the slope, which is the rate of change.

• b is the y-intercept, which is the value of y when x = 0.

Item 7:

From x = -3 to x = 1, when x changes by 4, y changes by 0.8, hence the slope is:

$m = \frac{0.8}{4} = 0.2$.

Then:

$y = 0.2x + b$

When x = 1, y = 0.2, which is used to find b. Hence:

$0.2 = 0.2 + b$

$b = 0$

Hence, $y = 0.2x$.

Item 8:

From x = -5 to x = -2, when x changes by 3, y changes by 9, hence the slope is:

$m = \frac{9}{3} = 3$.

Then:

$y = 3x + b$

When x = 4, y = 17, which is used to find b. Hence:

$17 = 3(4) + b$

$b = 5$

Hence, $y = 3x + 5$.

Item 9:

From x = -5 to x = -2, when x changes by 3, y changes by -6, hence the slope is:

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

Then:

$y = -2x + b$

When x = 8, y = -18, which is used to find b. Hence:

$-18 = -2(8) + b$

$b = -2$

Hence, $y = -2x - 2$.

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