1. Whint is the equmtion of the tine that pastes therecroh the points \( (9-8) \) and \( (10,-7) 7 \) Write vour inswigr in slope-intercert form. \[ \frac{-7-8^{\prime}}{10-9}=\frac{1}{1}=1 \] \[ \begin{array}{l}\ny=m \times i b \ -7=1(10)+b \ -7=10+b \ -7+10=-17 \end{array} \] 4. What is the equation of the line that passes through the points \( (-5,-6) \) and \( (-5,1) \) ? 5. What is the equation of the line that passes through the points \( (-10,1) \) and \( (1,1) \) ? 7. What is the equation of the line that passes through the points \( (-10,5) \) and \( (6,29) \) ? Write your answer in slope-intercept form.

Sure, let's address each of your questions step by step. I'll also correct and clarify the solution for **Question 1**. --- ### **1. Equation of the Line Passing Through the Points \( (9, -8) \) and \( (10, -7) \)** **Step 1: Find the Slope (m)** The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the given points: \[ m = \frac{-7 - (-8)}{10 - 9} = \frac{1}{1} = 1 \] **Step 2: Use the Slope-Intercept Form to Find \( b \)** The slope-intercept form of a line is: \[ y = mx + b \] Using one of the points, say \( (10, -7) \): \[ -7 = (1)(10) + b \\ -7 = 10 + b \\ b = -7 - 10 \\ b = -17 \] **Final Equation:** \[ y = x - 17 \] *Note:* In your initial attempt, there was a small arithmetic error when solving for \( b \). Specifically, \( -7 + 10 \) equals \( 3 \), but since the equation is \( -7 = 10 + b \), solving for \( b \) correctly gives \( b = -17 \). --- ### **4. Equation of the Line Passing Through the Points \( (-5, -6) \) and \( (-5, 1) \)** Both points have the same \( x \)-coordinate (\( x = -5 \)), which means the line is **vertical**. **Equation of a Vertical Line:** \[ x = -5 \] *Note:* Vertical lines have an undefined slope and cannot be expressed in the slope-intercept form \( y = mx + b \). --- ### **5. Equation of the Line Passing Through the Points \( (-10, 1) \) and \( (1, 1) \)** Both points have the same \( y \)-coordinate (\( y = 1 \)), which means the line is **horizontal**. **Equation of a Horizontal Line:** \[ y = 1 \] *Note:* Horizontal lines have a slope of \( 0 \) and their equation is straightforwardly \( y = \) constant. --- ### **7. Equation of the Line Passing Through the Points \( (-10, 5) \) and \( (6, 29) \)** **Step 1: Find the Slope (m)** \[ m = \frac{29 - 5}{6 - (-10)} = \frac{24}{16} = \frac{3}{2} \] **Step 2: Use the Slope-Intercept Form to Find \( b \)** Using the point \( (6, 29) \): \[ 29 = \left(\frac{3}{2}\right)(6) + b \\ 29 = 9 + b \\ b = 29 - 9 \\ b = 20 \] **Final Equation:** \[ y = \frac{3}{2}x + 20 \] *Alternatively, in decimal form:* \[ y = 1.5x + 20 \] --- Feel free to ask if you have any more questions or need further clarification!