7. The equation of a line describes the relationship between the \( x \)-and \( y \)-coordinates of the points on the line. \( 5-7 \) HW eTool Homework Help a. Plot the points \( (3,-1),(3,2) \), and \( (3,4) \) and draw the line that passes through them. State the coordinates of two more points on the line. Then answer it question: What will be true of the coordinates of any other point on this line? Now write an equation that says exactly the same thing. (Do not worry if it is simple! If it accurately describes all the points on this line, it is correct.) b. Plot the points \( (5,-1),(1,-1) \), and \( (-3,-1) \). What is the equation of the line that goes through these points? c. Choose any three points on the \( y \)-axis. What is the equation of the line that goes through those points?

Let's solve the problem step by step. ### Part a 1. **Plotting the Points**: The points given are \( (3, -1) \), \( (3, 2) \), and \( (3, 4) \). - All these points have the same \( x \)-coordinate, which is \( 3 \). This means they are vertically aligned on the graph. 2. **Drawing the Line**: Since all points share the same \( x \)-coordinate, the line that passes through these points is a vertical line. 3. **Finding Two More Points**: Any other points on this line will also have the same \( x \)-coordinate of \( 3 \). For example, we can choose: - \( (3, 0) \) - \( (3, 5) \) 4. **What is True for Any Other Point on This Line**: The coordinates of any other point on this line will have the form \( (3, y) \), where \( y \) can be any real number. 5. **Equation of the Line**: The equation that describes this line is: \[ x = 3 \] ### Part b 1. **Plotting the Points**: The points given are \( (5, -1) \), \( (1, -1) \), and \( (-3, -1) \). - All these points have the same \( y \)-coordinate, which is \( -1 \). This means they are horizontally aligned on the graph. 2. **Equation of the Line**: The equation that describes this horizontal line is: \[ y = -1 \] ### Part c 1. **Choosing Points on the \( y \)-axis**: Any three points on the \( y \)-axis can be chosen. For example, let's choose: - \( (0, 2) \) - \( (0, -3) \) - \( (0, 5) \) 2. **Equation of the Line**: Since all these points have the same \( x \)-coordinate of \( 0 \), the equation of the line that goes through these points is: \[ x = 0 \] ### Summary of Answers - **Part a**: The equation is \( x = 3 \). - **Part b**: The equation is \( y = -1 \). - **Part c**: The equation is \( x = 0 \).