Question

Write an equation from slope-intercept form ( y=mx+b ) from the table below.
x-y
0-2
5- -3
10- -8
15- -13

Answer 1

To write an equation in slope-intercept form (y = mx + b), we first need to determine the slope \( m \) and the y-intercept \( b \) using the data provided in the table.

From the table, we have the following points:

1. (0, 2)
2. (5, -3)
3. (10, -8)
4. (15, -13)

### Step 1: Calculate the slope (m)

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Let's use the points (0, 2) and (5, -3):

- \( (x_1, y_1) = (0, 2) \)
- \( (x_2, y_2) = (5, -3) \)

Now plug in the values:

\[
m = \frac{-3 - 2}{5 - 0} = \frac{-5}{5} = -1
\]

### Step 2: Calculate the y-intercept (b)

The y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the first point (0, 2), we see that when \( x = 0 \), \( y = 2 \). Therefore, \( b = 2 \).

### Step 3: Write the equation

Now that we have the slope \( m = -1 \) and the y-intercept \( b = 2 \), we can write the equation in slope-intercept form:

\[
y = -1x + 2
\]

or simply:

\[
y = -x + 2
\]

This is the equation that represents the data from the table.