Question

Tell whether the data in the table can be modeled by a linear equation. Explain.

Answer 1

Answer:

y = -3x + 7

Step-by-step explanation:

Choosing two points from the given table:

Let (x1, y1) = (-3, 16)

(x2, y2) = (-1, 10)

Plug these given values into the slope formula:

m = (y2 - y1)/(x2 - x1)

   = (10 - 16) / (-1 - (-3))

   = -6 / (-1 + 3)

   = -6/2

   = -3

Therefore, the slope is -3.

Next, choose one of the points and plug into the point-slope form:

Let's use (-1, 10) as (x1, y1):

y - y1 = m(x - x1)

y - 10 = -3(x - (-1))

y - 10 = -3(x + 1)

y - 10 = -3x - 3

Add 10 on both sides to isolate y:

y - 10 + 10 = -3x - 3 + 10

y = -3x + 7