Question

A function is represented by the table. x y 3 -2 5 -26 7 -50 The rate of change of the function represented in the table is . For the given x- and y-values, the function is .

Answer 1

Explanation:

Here is your x/y table, a bit more organized:

x | 3 5 7

y | -2 -26 -50

The rate of change is the same thing as the slope. If the slope between coordinates 1 and 2 is the same as the slope between coordinates 2 and 3, we have a linear function in the form y = mx + b, where m is the slope and b is the y-intercept. We will have to solve for b if we want to use this form. Or we could use the point-slope form and not have to solve for b. Let's do that. But first things first. The slope:

Between the first 2 coordinates (3, -2) and (5, -26):

`m=(-26-(-2))/(5-3)=(-24)/(2)=-12`

Between coordinates 2 and 3 which are (5, -26) and (7, -50):

`m=(-50-(-26))/(7-5) =(-24)/(2)=-12`

The slopes are the same, so this in fact a linear function with m = -12. But that's all we have, so let's use the point-slope form of a line to write the equation:

`y-y_1=m(x-x_1)` where
`x_1` and
`y_1` are coordinates found in the table. Plugging in the first coordinate along with the slope of -12:

`y-(-2)=-12(x-3)` and

y + 2 = -12x + 36 and

y = -12x + 36 - 2 so the equation for the line in slope-intercept form is

y = -12x + 34

Regardless of which coordinate point you choose as your x1 and y1, I promise you that you will still get the same equation for the line!

Answer 2

hi its -12 and decreasing.