Question

Write an equation from slope-intercept form (

y
=
m
x
+
b
y=mx+b ) from the table below.

x
x
y
y
0
0
8
8
4
4
2
2
8
8
−
4
−4
12
12
−
10
−10





y

=
y =

x

+
x +

Answer 1

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

### Points from the Table

Let's list the coordinates from the table:

- (0, 8)
- (4, 4)
- (2, 2)
- (8, -4)
- (12, -10)

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

The slope \( m \) is calculated using the formula:

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

We can select any two points. Let's use the points (0, 8) and (4, 4) to calculate the slope:

\[
m = \frac{4 - 8}{4 - 0} = \frac{-4}{4} = -1
\]

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

Using the slope \( m = -1 \) and one of the points (let's use (0, 8)), we can substitute into the slope-intercept form of the equation to find \( b \):

\[
y = mx + b
\]

Substituting \( x = 0 \) and \( y = 8 \):

\[
8 = -1(0) + b
\]
\[
b = 8
\]

### Final Equation

Now, we plug \( m \) and \( b \) back into the slope-intercept form \( y = mx + b \):

\[
y = -1x + 8
\]

or simply:

\[
y = -x + 8
\]

So the equation from the table in slope-intercept form is:

\[
y = -x + 8
\]