The best way to learn about the equations of lines is to experiment.
Use this online graphing calculator to perform your experiments. Keep a record of the things you learn about horizontal lines and their equations.
On the graphing calculator, next to the red square, there is y1 = then an empty box. In the box, type 2. Click on the orange Graph button. The calculator will graph y = 2. Write down a description of what the graph looks like. Be specific.
Without deleting the 2 from the first box, in the box next to y2 = type 5. Click on Graph. The calculator will graph y = 2 and y = 5. How is the new graph different from the old one?
Without deleting anything from the boxes, in the box next to y3 = type 8. How is this graph different from the first two? What is the equation of this graph we just added?
What do you think will happen if we type in 7 in the last box? What is the equation of this graph we just added?
Check to see if you were right.
What do you think will happen if we type in -2 in the last box?
In the last box, delete the 7 and type in -2. Check to see if your answer was right. The equation of this graph is y = -2.
Experiment by changing the number in the box (this number is called the y-intercept, can you figure out why?) to other numbers including negative numbers, fractions, and decimals. Continue experimenting until you can figure out what the graph of the equation will look like without having to graph it.
Carefully examine all the horizontal lines. Then, upload your comment about this topic:
If you have a graph of a horizontal line, how can you quickly find its equation?
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