Question

x-y
0-4
6-6
12-8
18-10
Write an equation from slope-intercept form (y=mx+b ) from the table below.

Answer 1

To find the equation in slope-intercept form \( y = mx + b \) from the given data points, we first need to calculate the slope \( m \) and the y-intercept \( b \).

### Step 1: Identify the points from the table

Based on your table, the points are:
- (0, 4)
- (6, 6)
- (12, 8)
- (18, 10)

### Step 2: Calculate the slope \( m \)

The formula for the slope \( m \) is:

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

We can use any two points. Let's take the points (0, 4) and (6, 6):

\[
m = \frac{6 - 4}{6 - 0} = \frac{2}{6} = \frac{1}{3}
\]

### Step 3: Calculate the y-intercept \( b \)

Using the slope \( m = \frac{1}{3} \) and one of the points (0, 4), we can find \( b \):

Since \( x = 0 \), we substitute into the equation:

\[
y = mx + b \Rightarrow 4 = \left(\frac{1}{3}\right)(0) + b \Rightarrow b = 4
\]

### Step 4: Write the equation

Now we have the values for \( m \) and \( b \):

\[
y = \frac{1}{3}x + 4
\]

### Final Equation

Thus, the equation in slope-intercept form based on the data provided is:

\[
y = \frac{1}{3}x + 4
\]