Question

The graph of a linear function passes through the points (6,
–7) and (9, –13/2). Write an equation for the function in the form y = mx + b.
y =

Answer 1

To find the equation of the linear function that passes through the points (6, –7) and (9, –13/2), we first need to calculate the slope \( m \) of the line using the formula:

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

Here, \((x_1, y_1) = (6, -7)\) and \((x_2, y_2) = (9, -\frac{13}{2})\).

Substituting these coordinates into the formula:

\[
m = \frac{-\frac{13}{2} - (-7)}{9 - 6}
\]

We can simplify this step by step. First, convert -7 to a fraction:

\[
-7 = -\frac{14}{2}
\]

Now substituting back:

\[
m = \frac{-\frac{13}{2} + \frac{14}{2}}{3} = \frac{\frac{1}{2}}{3} = \frac{1}{6}
\]

Thus, the slope \( m \) is \( \frac{1}{6} \).

Next, we use the point-slope form of the equation:

\[
y - y_1 = m(x - x_1)
\]

Using the point (6, -7):

\[
y - (-7) = \frac{1}{6}(x - 6)
\]

This simplifies to:

\[
y + 7 = \frac{1}{6}x - 1
\]

Now, subtract 7 from both sides:

\[
y = \frac{1}{6}x - 1 - 7
\]

This gives:

\[
y = \frac{1}{6}x - 8
\]

Thus, the equation of the linear function in the form \( y = mx + b \) is:

\[
\boxed{y = \frac{1}{6}x - 8}
\]