standard_description: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
problem_activity: Problem 1
You and a friend are going for a run along a path. You both run at the same exact speed, but your friend starts 100 yards ahead of the starting point which is where you start.
The graph below is a sketch of your and your friend’s distance traveled from the starting point over time. When will you and your friend be the same distance from the starting point? Explain your answer using the graph.
[IMG]
Problem 2
Graph the system of equations below.
| $${y={1\over3}(x-6)}$$                        $${6y=2x-12}$$ | .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/09/23/slice-1-2022-09-23t114209772.png |
|--------------------------------------------------------------|------------------------------------------------------------------------------------------------------|
Anika was not sure how to interpret the graph of the system. She thought that since there was only one line visible in the graph then there were no solutions to the system of equations. Do you agree with Anika's reasoning? Explain why or why not.
Problem 3
Consider the equation
$$y = \frac{2}{5} x + 1$$
. Write a second linear equation to create a system of equations that has:
a.   Exactly one solution
b.   No solutions
c.   Infinite solutions


aligns: no