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

Answer 1

To analyze the data in the provided table, we need to determine the rate of change, the y-intercept, and the equation of the line in slope-intercept form.

**Given Points:**
1. (-2, 80)
2. (-1, 70)
3. (2, 40)
4. (5, 10)

**1. Calculate the rate of change (slope):**

To find the slope (rate of change), we can use two of the points. Let's use the points (-2, 80) and (5, 10):

The formula for the slope \( m \) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (-2, 80) as \((x_1, y_1)\) and (5, 10) as \((x_2, y_2)\):
\[
m = \frac{10 - 80}{5 - (-2)} = \frac{-70}{7} = -10
\]

**The rate of change = -10.**

**2. Find the y-intercept (b):**

The y-intercept is the value of \( y \) when \( x = 0 \). We can use the point-slope form, using the slope we just calculated (-10) and one of the points to find the y-intercept.

Using the point (-2, 80):
\[
y - y_1 = m(x - x_1)
\]
Substituting:
\[
y - 80 = -10(x + 2)
\]
Expanding this:
\[
y - 80 = -10x - 20
\]
\[
y = -10x + 60
\]

**The y-intercept = \( b = 60 \).**

**3. The equation of the line in slope-intercept form is:**
\[
y = -10x + 60
\]

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