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 find the rate of change, the y-intercept, and the equation of the line in slope-intercept form (y = mx + b) using the provided points, we follow these steps:

### Step 1: Rate of Change (Slope)
The rate of change (slope, m) can be calculated using two points from the table. The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

We can use the points (-2, 80) and (5, 10):

1. Point 1: (-2, 80) \(\Rightarrow x_1 = -2\), \(y_1 = 80\)
2. Point 2: (5, 10) \(\Rightarrow x_2 = 5\), \(y_2 = 10\)

Plugging values into the slope formula:

\[
m = \frac{10 - 80}{5 - (-2)} = \frac{-70}{7} = -10
\]

**The rate of change (slope) = -10**


### Step 2: Y-Intercept
To find the y-intercept (b), we can use the slope-intercept form of the equation \(y = mx + b\) and one of the points. Let's use the point (5, 10):

Using the formula:

\[
10 = -10(5) + b
\]

Calculating the right-hand side:

\[
10 = -50 + b \implies b = 10 + 50 = 60
\]

**The y-intercept = 60**

### Step 3: Slope-Intercept Form Equation
Now that we have the slope \(m = -10\) and the y-intercept \(b = 60\), we can write the slope-intercept form of the equation as:

\[
y = -10x + 60
\]

**The equation of the line in slope-intercept form 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**