### Home > GB8I > Chapter 5 Unit 6 > Lesson INT1: 5.1.1 > Problem5-7

5-7.

The equation of a line describes the relationship between the $x$ and $y$coordinates of the points on the line.

1. Plot the points $(3,-1),(3,2),\text{ and }(3,4)$ and draw the line that passes through them. State the coordinates of two more points on the line. Then answer this 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 very simple! If it accurately describes all the points on this line, it is correct.)

Two more points are $(3,0)$ and $(3,3)$.

Look closely at the $x$-coordinate, but you should name two others.

All of the points will have $3$ as an $x$-coordinate.

The equation is $x = 3$.

2. Plot the points $(5, –1), (1, –1), \text{ and }(–3, –1)$. What is the equation of the line that goes through these points?

Look closely at the $y$-coordinate.

3. Choose any three points on the $y$axis. What is the equation of the line that goes through those points?

Remember that all points on the $y$-axis have $0$ for their $x$-coordinate.

The equation is $x = 0$.

Use the eTool below to plot points to help discover the equation for each situation.
Click on the link at right for the full eTool version:  (Desmos)