Question

Write an equation from slope-intercept form (y=mx+b ) from the table below.
x y
0, 8
4, 2
8, -4
12, 10

Answer 1

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

The points from the table are:
1. (0, 8)
2. (4, 2)
3. (8, -4)
4. (12, 10)

### 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 first two points: (0, 8) and (4, 2).

\[
m = \frac{2 - 8}{4 - 0} = \frac{-6}{4} = -\frac{3}{2}
\]

### Step 2: Find the y-intercept \( b \)

The y-intercept \( b \) can be determined using one of the points. Let's use the point (0, 8):

Since we're using the slope-intercept form \( y = mx + b \):

At \( x = 0 \), \( y = 8 \).

So,

\[
8 = -\frac{3}{2}(0) + b \implies b = 8
\]

### Step 3: Put it all together

Now that we have \( m = -\frac{3}{2} \) and \( b = 8 \), we can write the equation in slope-intercept form.

\[
y = -\frac{3}{2}x + 8
\]

### Final Answer
The equation in slope-intercept form is:

\[
y = -\frac{3}{2}x + 8
\]