C The constant rate of change of y with respect to x is said to be the value of this ratio,- This value is often referred to as m. Ay Az

To say that two quantities are changing together at a constant rate of change does not imply that the quantities themselves are proportional. In contrast, it is true that if two quantities are proportional, it follows that the two quantities are changing together at a constant rate of change. We begin this lesson by reviewing what it means for the values of two quantities, z and y, to change together at a constant rate of change. We continue by reviewing the idea of proportionality and exploring how the ideas of constant rate of change and proportionality are related. We then practice using these ideas in applied contexts. To illustrate, let's consider a situation where a and y are varying together at a constant rate of change and we know that the point (5, 3) or the values z = 5 and y = 3 are in the relationship. I Suppose z and y are varying together at a constant rate of change and we know that the point (5, 3) or the values z = 5 and y = 3 are in the relationship. Note: You can interact with the applet by moving the purple "X" on the horizontal axis to represent varying the value of 2. 10 y 8 6 4 2 2 4 (5.3) Ax 6 Ay 8 2 10 Drag the purple X on the z-axis to vary the value of a 9 Show Hypotenuse Az = 2 Ay = 4/na. Drag the purple X on the z-axis to vary the value of a from z = 5 to z = 1. Determine the value of Az as a varies from 5 to z = 1. Az -4 b. Drag the purple X on the z-axis to vary the value of z from z = 5 to z = 1 and notice how y varies on this interval. As the value z varies from z 5 to = 1, the value of y decreases ✓✓ from 3 c. Determine the value of Ay as a varies from 5 to z = 1. Ay 8 Ay Ar Preview d. Determine the value of as a varies over the interval from 5 to 1, Ay Az - 2 Preview Preview e. As a and y vary together at a constant rate of change, the ratio of Ay tz (also written Preview 2deltax to 11 ✔ -) is always 2 Preview f. As a and y vary together at a constant rate of change, then Ay g. The constant rate of change of y with respect to z, as represented in the above linear graph, is-2 Hint Preview