Question

Write an equation from slope-intercept form (

𝑦
=
𝑚
𝑥
+
𝑏
y=mx+b ) from the table below. Click Here for Help Video.

𝑥
x
𝑦
y
9
9
−
12
−12
18
18
−
19
−19
27
27
−
26
−26





𝑦

=
y =

𝑥

+
x +

Answer 1

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

Here are the data points from the table:

- (9, 9)
- (18, -19)
- (27, -26)

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

The slope formula is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the first two points (9, 9) and (18, -19):
- \( x_1 = 9 \)
- \( y_1 = 9 \)
- \( x_2 = 18 \)
- \( y_2 = -19 \)

Now, we can substitute in the values:
\[
m = \frac{-19 - 9}{18 - 9} = \frac{-28}{9} = -\frac{28}{9}
\]

Next, let's use the second and third points (18, -19) and (27, -26):
- \( x_1 = 18 \)
- \( y_1 = -19 \)
- \( x_2 = 27 \)
- \( y_2 = -26 \)

Substituting those values:
\[
m = \frac{-26 - (-19)}{27 - 18} = \frac{-26 + 19}{9} = \frac{-7}{9}
\]

Now we need to ensure we have consistent slopes. Using the first point and any of the derived points will give us the same slope due to being linear.

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

We can use one of the points and the slope to find \( b \). Let's use the point (9, 9).

Substitute into the equation \( y = mx + b \):
\[
9 = -\frac{28}{9}(9) + b
\]

Calculating it:
\[
9 = -28 + b
\]
\[
b = 9 + 28 = 37
\]

### Final Equation

Now we have \( m = -\frac{28}{9} \) and \( b = 37 \).

Thus, the equation in slope-intercept form is:
\[
y = -\frac{28}{9}x + 37
\]

If preferred, we can also express it as:
\[
y = -\frac{28}{9}x + 37
\]