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).
- 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 \((x_2, y_2) = (-3, -1)\):
\[ m = \frac{-1 - 4}{-3 - 2} = \frac{-5}{-5} = 1 \]
- 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 \( b \):
\[ 4 = 2 + b \] \[ b = 4 - 2 = 2 \]
- 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:
\[ \boxed{y = x + 2} \]