A student earns $0.65 for each mistake she finds in a text. Sketch the equation of direct variation.
An equation of direct variation is of the form
M = k X
where k us a constant. In your case M might be total money earned and X is the number of students.
Clearly M = 0.65 X
The graph is a straignt line through the origin with slope 0.65. It goes through the points
M = 0, X = 0 (the origin)
and
M = 13, X = 20
To sketch the equation of direct variation for this problem, we can use the formula M = kX, where M represents the total money earned and X represents the number of mistakes found.
In this case, we are given that each mistake earns the student $0.65. So, we can rewrite the equation as M = 0.65X.
To graph this equation, we need to determine two points on the line. Let's start with the origin (0,0).
When X = 0 (no mistakes found), M = 0 (no money earned). Therefore, the point (0,0) lies on the line.
Next, let's choose another point on the line, such as when X = 20.
When X = 20 mistakes found, we can calculate M as:
M = 0.65(20)
M = 13
So, the point (20,13) lies on the line as well.
Now, we can plot these two points on a graph and draw a straight line connecting them. The slope of the line, which represents the rate of change, is 0.65.