Rates, Graphs, Slopes, and Equations The concept of slope comes from the idea of a constant rate of change. Formally, the slope of the line connecting two points (x,y,) and (x, y,) is (x2, Y2) defined as the ratio ソ2ー Y 一 X, - x, (xp Y1) The numerator of this fraction is sometimes referred to as the change in y or the rise. The denominator is called the change in x or the run. In this activity, you will work with rates and slopes, exploring their connections to graphs and formulas. 1. A jogger is moving at a rate of 500 feet per minute. That's about 6 miles per hour. a. Plot a graph showing the distance the jogger has traveled (in feet) as a function of t (in minutes). Use t = 0 as the time when the jogger starts. b. Find an equation for this function. c. Choose two points on your graph and use their coordinates to compute the slope of the graph.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.