Question

x y

-2 80
-1 70
2 40
5 10

Answer the questions using the table.

the rate of change =
the y−intercept =
the equation of the line is =

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the rate of change, we can use the formula:

Rate of Change = (Change in y) / (Change in x)

Looking at the table, we can see that the change in y between each pair of values is -10. And the change in x is 1 between each pair. So the rate of change is:

Rate of Change = (-10) / (1) = -10

To find the y-intercept, we can look at the table for the value of y when x = 0. However, there is no value of x = 0 in the table. Therefore, we cannot determine the y-intercept from the given data.

Lastly, to find the equation of the line, we can use the slope-intercept form:

y = mx + b

where m is the rate of change and b is the y-intercept. Since we know the rate of change is -10 but not the y-intercept, we cannot determine the equation of the line with the given information.

Answer 2

are you sure?

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion in my previous response. Let me correct it.

To find the rate of change, we can again use the formula:

Rate of Change = (Change in y) / (Change in x)

From the table, we can see that the change in y between each pair of values is -10, and the change in x is 1 between each pair. So the rate of change is:

Rate of Change = (-10) / (1) = -10

To find the y-intercept, we can look at the table for the value of y when x = 0. However, there is no value of x = 0 in the table. Therefore, we still cannot determine the y-intercept from the given data.

Lastly, to find the equation of the line, we can use the point-slope form:

y - y₁ = m(x - x₁)

where (x₁, y₁) is a point on the line and m is the rate of change. We can choose any point from the table to substitute into the equation. Let's use the point (2, 40):

y - 40 = -10(x - 2)

Simplifying, we have:

y - 40 = -10x + 20

Moving the terms around, we get:

y = -10x + 60

So, the equation of the line is y = -10x + 60.