Question

Identify the equation of the linear function through the points ​(- 2​,- 7​) and ​(1​,2​). Then state the rate of change of the function. What is the equation of the linear​ function?

A. y = 3x - 1
B. y = - 3x - 1
C. y = 3x + 1
D. y = -3x + 1

The rate of change is ( ? ).

Answer 1

The equation of line is y = 3 x - 1 , i.e option A .

The rate of change = m = 3

Explanation:

Given as :

The points are

(
`x_1`,
`y_1` ) = (- 2, -7)

(
`x_2`,
`y_2` ) = (1 , 2)

Let The slope = m

Now, The slope is calculated in points form

So, Slope =
`(y_2-y_1)/(x_2-x_1)`

I.e m =
`(2-(-7))/(1-(-2))`

or, m =
`(9)/(3)`

I.e m = 3

So, The slope of points = m = 3

I,e Rate of change = m = 3

Now, the equation of line in slope - point form can be written as

y -
`y_1` = m ( x -
`x_1`)

where m is the slope of line

i.e y - (-7) = ( 3 ) × ( x - (-2) )

or, y + 7 = 3 × (x + 2)

∴ y + 7 = 3 x + 6

Or, y = 3 x + 6 - 7

Or, y = 3 x - 1

So, The equation of line is y = 3 x - 1

Hence, The equation of line is y = 3 x - 1 , i.e option A .

And The rate of change = m = 3 Answer