Question

A graph with (2 , 4) and (-3 , -1)

Write the equation of the linear function shown on the graph. Enter your answer in y = mx + b form.

Answer 1

To find the equation of the linear function that passes through the points (2, 4) and (-3, -1), we need to determine the slope (m) and the y-intercept (b).

1. **Find the slope (m):**

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Let \((x_1, y_1) = (2, 4)\) and \((x_2, y_2) = (-3, -1)\):

\[
m = \frac{-1 - 4}{-3 - 2} = \frac{-5}{-5} = 1
\]

2. **Use the slope and one of the points to find the y-intercept (b):**

Using the point (2, 4) and the slope \( m = 1 \), we can use the point-slope form of a line \( y = mx + b \):

\[
4 = 1(2) + b
\]

Now solve for \( b \):

\[
4 = 2 + b
\]
\[
b = 4 - 2 = 2
\]

3. **Write the equation in slope-intercept form \( y = mx + b \):**

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

\[
y = 1x + 2
\]

Therefore, the equation of the linear function is:

\[
\boxed{y = x + 2}
\]