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

Answer:

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

The rate of change = m = 3

Step-by-step 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 = $\dfrac{y_2-y_1}{x_2-x_1}$

I.e m = $\dfrac{2-(-7)}{1-(-2)}$

or, m = $\dfrac{9}{3}$

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