Question

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

Answer the questions using the table.

(3 points)
the rate of change =


the y−intercept =

the equation of the line in slope intercept form is


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Answer 1

To analyze the data in the table and answer the questions, we can first identify that we have a set of points:

1. \((-2, 80)\)
2. \((-1, 70)\)
3. \((2, 40)\)
4. \((5, 10)\)

### 1. To find the rate of change (slope):

The rate of change (slope) \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let's use the first two points \((-2, 80)\) and \((-1, 70)\):

\[
m = \frac{70 - 80}{-1 - (-2)} = \frac{-10}{1} = -10
\]

Thus, the rate of change is \(-10\).

### 2. To find the y-intercept:

Using one of the points and the slope, we can express it in point-slope form and then convert it to slope-intercept form \(y = mx + b\).

From our earlier calculation, the slope \(m = -10\). Using the point \((-1, 70)\):

Using the linear equation form:
\[
y - y_1 = m(x - x_1)
\]
Substituting the slope and the point:
\[
y - 70 = -10(x + 1)
\]
Expanding it out:
\[
y - 70 = -10x - 10
\]
\[
y = -10x + 60
\]
So, the y-intercept \(b = 60\).

### 3. The equation of the line in slope-intercept form \(y = mx + b\):

From our calculations, the slope \(m = -10\) and the y-intercept \(b = 60\). The equation of the line is:
\[
y = -10x + 60
\]

### Summary of Answers:

- The rate of change = \(-10\)
- The y-intercept = \(60\)
- The equation of the line in slope-intercept form is \(y = -10x + 60\)