Question 10 of 14, Step 1 of 1 Find the equation in slope-intercept form for the line passing through the points with the given coordinates. Answer

Sure, I'd be happy to help you find the equation of the line in slope-intercept form (\( y = mx + b \)) that passes through two given points. To provide an accurate answer, I'll need the coordinates of those points. However, I can guide you through the general steps to find the equation: ### Steps to Find the Equation of a Line Passing Through Two Points 1. **Identify the Coordinates:** Let's denote the two points as \( P_1(x_1, y_1) \) and \( P_2(x_2, y_2) \). 2. **Calculate the Slope (\( m \)):** The slope of the line is determined by the change in \( y \) divided by the change in \( x \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] 3. **Use the Slope-Intercept Form:** The slope-intercept form of a line is: \[ y = mx + b \] You already have \( m \) from the previous step. 4. **Solve for the Y-Intercept (\( b \)):** Substitute one of the points and the slope into the equation to solve for \( b \): \[ y_1 = m \cdot x_1 + b \\ b = y_1 - m \cdot x_1 \] 5. **Write the Final Equation:** Plug the values of \( m \) and \( b \) back into the slope-intercept form to get the equation of the line. ### Example Let's go through an example for clarity. **Given Points:** - \( P_1(2, 3) \) - \( P_2(4, 7) \) **1. Calculate the Slope (\( m \)):** \[ m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2 \] **2. Use the Slope-Intercept Form:** \[ y = 2x + b \] **3. Solve for \( b \) Using Point \( P_1(2, 3) \):** \[ 3 = 2 \cdot 2 + b \\ 3 = 4 + b \\ b = 3 - 4 \\ b = -1 \] **4. Write the Final Equation:** \[ y = 2x - 1 \] So, the equation of the line passing through the points \( (2, 3) \) and \( (4, 7) \) is \( y = 2x - 1 \). ### If You Provide the Coordinates If you provide the specific coordinates of the two points you're working with, I can give you a tailored solution to find the exact equation of the line passing through them.