Algebra I Task – Unit 5 Slope, Equations, and Graphs of Lines – Stairs and Ramps
A.6 The student will
a. determine the slope of a line when given an equation of the line, the graph of the line, or two
points on the line;
b. write the equation of a line when given the graph of the line, two points on the line, or the slope
and a point on the line; and
c. graph linear equations in two variables.
Teacher Notes: The goal of this task is for the students to apply their knowledge of slope and equations of
lines to create equations for a set of stairs and their companion ramp. If students create equations for the
first part of the task that are not realistic, but then use those equations to correctly address the second
and third parts of the task, they should receive full credit for those parts.
Slope, Equations, and Graphs of Lines – Stairs and Ramps
Problem: Both stairs and ramps can be used to connect two different levels, but they do not have to have
the same rate of change.
Task 1: Create a graph and write the corresponding equations that would show the two lines created by
the stairs and ramp in the picture above. How did you decide on your equations?
Task 2: What do the lines have in common? What is different? Why?
Task 3: The guidelines for wheelchair ramps require that a 1-foot increase in vertical height requires a
horizontal distance of 12 feet. Would either of your lines meet that requirement? How do you know?