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
Julia, Keller, and Isreal are volunteer firefighters. On Saturday, the volunteer fire department held its annual coin drop fundraiser at a streetlight. After one hour, Keller had collected $42.50 more than Julia, and Isreal had collected $15 less than Keller. The three firefighters collected $125.95 in total. How much did each person collect?
Problem 2
Your parents are redecorating the dining room and want to place two rectangular pictures, each measuring 25 inches across, on the wall, which measures
$${10 {2\over3}}$$
feet long. They want to place the pictures so that the distance between the pictures and the distances from each picture to the end of the wall are the same, as shown in the diagram below.
[IMG]
Determine the distance each picture should be placed from the ends of the wall. Explain the strategy that you used.
Problem 3
Three toothpick configurations are shown in the chart below.
[IMG]
a.   Extend the pattern to complete the chart.
b.   How many toothpicks will be in the 10th design?
c.   Write an expression to represent the number of toothpicks in the
$$n$$
th design.
d.   Which design will have 175 toothpicks? Write and solve an equation.


aligns: no