Question

Can you come up with the equation for the table to the left in y=m+ b form?
x 0,2,4,8
y 6,5,4,2

Answer 1

To find the equation of the line in the form \( y = mx + b \) based on the given data points, we first need to calculate the slope \( m \) using two of the given points.

Let's use the points \( (0, 6) \) and \( (8, 2) \):

1. **Calculate the slope \( m \)**:
The formula for the slope \( m \) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 6) \) and \( (8, 2) \):
\[
m = \frac{2 - 6}{8 - 0} = \frac{-4}{8} = -\frac{1}{2}
\]

2. **Use the slope-intercept form to find \( b \)**:
We know that \( y = mx + b \), and we can use one of the points to solve for \( b \). Let’s use the point \( (0, 6) \):
\[
6 = -\frac{1}{2}(0) + b
\]
Therefore, \( b = 6 \).

3. **Write the equation in slope-intercept form**:
Now that we have \( m \) and \( b \), we can write the equation:
\[
y = -\frac{1}{2}x + 6
\]

Thus, the equation for the table is:
\[
y = -\frac{1}{2}x + 6
\]