Question

Given the following two ordered pairs calculate the rate of the function.
(−9, −4) and (−3, −16)
Enter your answer in the box.
M=

Given the linear function equation state the function rate.
y=−7x+1
Enter your answer in the box.
M=

Given the linear function table state the y-intercept.
x= -2, -1, 0, 1, 2
y=-6, 0, 6, 12, 18
Enter your answer in the box.
b=

Given the linear function Table state the function rate.
x= -2, -1, 0, 1, 2
y=-6, 0, 6, 12, 18
Enter your answer in the box.
m=

Select the linear function equation for the table.
x= -4, -3, -2, -1, 0
y= 7, 4, 1, -2, -5

y=−5x−3

y=3x+5

y=5x+3

y=−3x−5

Answer 1

Linear functions are functions that have uniform and constant rates.

(a) Ordered pairs

The ordered pair is given as (-9,-4) and (-3,-16).

The slope (m) is calculated as:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m = \frac{-16 --4}{-3--9}$

$m = \frac{-12}{6}$

$m = -2$

Hence, the slope (m) is 2

(b) The rate of y = -7x + 1

The function is given as $y = -7x + 1$

A linear function is represented as:

$y = mx + b$

Where m represents the slope/rate

By comparison

$m = -7$

Hence, the rate (m) is -7

(c) The y-intercept of a linear function

The y-intercept of a linear function is where the x-value is 0

From the table,

y = 6 when x = 0

Hence, the y-intercept (b) is 6

(d) Rate of a linear function

From the table, we have the following ordered pairs

(2,18) and (0,6).

The slope (m) is calculated as:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m = \frac{6 -18}{0-2}$

$m = \frac{-12}{-2}$

$m = 6$

Hence, the slope (m) is 6

(e) Equation of a linear function

From the table, we have the following ordered pairs

(0,-5) and (-3,4).

The slope (m) is calculated as:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m = \frac{4 --5}{-3-0}$

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

$m = -3$

The equation is then calculated as:

$y = m(x - x_1) + y_1$

So, we have:

$y = -3(x - 0) -5$

$y = -3x -5$

Hence, the linear equation is $y = -3x -5$

Read more about linear equations at:

https://brainly.com/question/14323743