Question

Answer the questions using the table.
x -2, -1, 2, 5
y 80, 70, 40, 10

(3 points)
the rate of change =


the y−intercept =

the equation of the line is
Answer
can u simplify this pls
Answer
so the rate of change is 10?
Answer
and the y intercept is 0
Answer
well is there an equation we could use. cause i don't need to fail this test
Answer
so since you did it this way, could u fine the y-intercept line and the equation
Answered by GPT 3.5
To find the rate of change, we can calculate the change in y divided by the change in x.

The change in y is 80 - 10 = 70.
The change in x is 5 - (-2) = 7.

So the rate of change is 70/7 = 10.

To find the y-intercept, we need to identify the value of y when x is 0. Looking at the table, we don't have a value for x=0. Therefore, we cannot determine the y-intercept from this table.

Without the y-intercept, we cannot determine the equation of the line.
Answered by GPT 3.5
Apologies for the confusion. Let's simplify the answers.

The rate of change is the change in y divided by the change in x. In this case, the change in y is 80 - 10 = 70, and the change in x is 5 - (-2) = 7. So, the rate of change is 70/7 = 10.

The y-intercept represents the value of y when x is 0. Since we don't have a value for x=0 in the table, we cannot determine the y-intercept.

Without the y-intercept, we cannot determine the equation of the line.
Answered by GPT 3.5
Yes, that's correct. The rate of change is 10.
Answered by GPT 3.5
Apologies for the confusion in my previous response. Since there is no information for the y-value when x is 0 in the given table, we cannot determine the y-intercept from this data. Therefore, we do not know the value of the y-intercept.
Answered by GPT 3.5
To find the equation of the line, we need to determine the slope (rate of change) and the y-intercept.

Since the rate of change is 10, we can use the point-slope form of the equation, which is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is any point on the line.

Let's choose one of the points from the table, like (-2, 80). Using this point and the slope (10), we can substitute them into the point-slope form:

y - 80 = 10(x - (-2))

Simplifying the equation further:

y - 80 = 10(x + 2)

Expanding the brackets:

y - 80 = 10x + 20

Finally, rearranging the equation to slope-intercept form (y = mx + b) by isolating y:

y = 10x + 20 + 80

y = 10x + 100

So, the equation of the line is y = 10x + 100.
Answered by GPT 3.5
Apologies for the confusion earlier. Let's go through the process again to find the y-intercept and the equation of the line.

To find the y-intercept, we need to identify the value of y when x is 0. Let's look at the table:

x | -2 -1 2 5
y | 80 70 40 10

Unfortunately, there is no value of x=0 in the table. Without a value for x=0, we cannot determine the y-intercept.

Since we don't have the y-intercept, we cannot directly determine the equation of the line.

Apologies for any confusion caused.