Question

Write an equation from slope-intercept form (y=mx+b ) from the table below.
x y
6,9
12, 13
18, 17

Answer 1

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

The points given are:
1. \( (6, 9) \)
2. \( (12, 13) \)
3. \( (18, 17) \)

**Step 1: Calculate the slope (m)**

The slope \( m \) can be calculated using the formula:

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

Let's use the first two points \( (6, 9) \) and \( (12, 13) \):

\[
m = \frac{13 - 9}{12 - 6} = \frac{4}{6} = \frac{2}{3}
\]

Now, let's check that the slope is consistent with the last two points \( (12, 13) \) and \( (18, 17) \):

\[
m = \frac{17 - 13}{18 - 12} = \frac{4}{6} = \frac{2}{3}
\]

Since the slope is consistent, the slope \( m \) is \( \frac{2}{3} \).

**Step 2: Calculate the y-intercept (b)**

Now we can use one of the points and the slope to find \( b \). Let's use the point \( (6, 9) \):

The equation of the line in slope-intercept form is:

\[
y = mx + b
\]

Substituting the known values:

\[
9 = \frac{2}{3}(6) + b
\]

Calculating \( \frac{2}{3}(6) \):

\[
9 = 4 + b
\]

Solving for \( b \):

\[
b = 9 - 4 = 5
\]

**Step 3: Write the equation**

Now we have both \( m \) and \( b \):

\[
m = \frac{2}{3}, \quad b = 5
\]

Thus, the equation in slope-intercept form is:

\[
y = \frac{2}{3}x + 5
\]