4. Write an equation to represent the linear function.

To write an equation representing a linear function, you'll typically use the slope-intercept form of a linear equation: \[ y = mx + b \] Where: - \( m \) is the **slope** of the line, representing the rate at which \( y \) changes with respect to \( x \). - \( b \) is the **y-intercept**, which is the value of \( y \) when \( x = 0 \). **Steps to Write the Equation:** 1. **Determine the Slope (\( m \)):** - If you have two points on the line, \((x_1, y_1)\) and \((x_2, y_2)\), the slope can be calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] 2. **Find the Y-Intercept (\( b \)):** - Once you have the slope, use one of the points and plug the values into the equation \( y = mx + b \) to solve for \( b \). 3. **Write the Final Equation:** - Substitute the values of \( m \) and \( b \) into the slope-intercept form. **Example:** Suppose you have two points on the line: \((2, 3)\) and \((4, 7)\). 1. **Calculate the Slope (\( m \)):** \[ m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2 \] 2. **Find the Y-Intercept (\( b \)):** - Using the point \((2, 3)\): \[ 3 = 2(2) + b \\ 3 = 4 + b \\ b = 3 - 4 \\ b = -1 \] 3. **Write the Equation:** \[ y = 2x - 1 \] **Thus, the linear equation representing the function is \( y = 2x - 1 \).** If you have specific points or additional information about the linear function you're working with, feel free to provide them, and I can help you formulate the exact equation!