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

y = 3x - 1

The rate of change of the function is 3.

Explanation:

The equation of the linear function through the points (- 2, - 7)and (1,2) will be given by

`(y - ( - 7))/(- 7 - 2) = (x - (- 2))/(- 2 - 1)`

⇒ (y + 7) = 3(x + 2)

⇒ y = 3x - 1 (Answer)

Now, the rate of change of the function is the slope of the line i.e. 3. (Answer)

We know the equation of a straight line which passes through the points
`(x_(1), y_(1))` and
`(x_(2), y_(2))` is given by

`(y - y_(1))/(y_(1) - y_(2)) = (x - x_(1))/(x_(1) - x_(2))`