Question

The following table shows the amount of money his friend Carl earns for different numbers of hours worked. How much money does Carl earn per hour? Show your work. You will not receive full credit for a correct answer without showing any work.










Draw a line on the graph below to show Carl’s earnings over time in hours. The following things must be done: plot the points, draw the line, label each axis, title the graph.

Answer 1

The equation of the graph that represent Carl’s earnings over time in hours is given by: y = 15x

The equation of a straight line is given by;

y = mx + b;

where y, x are variables, m is the slope of the graph and b is the y intercept.

Given the points from the table, we can determine the equation of the line graph using any two points.  Let y represent the money earned and x represent the time. Hence, using points (3, 45) and (10, 150):

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-45=\frac{75-45}{5-2}(x-3)\\\\y-45=15(x-3)\\\\y = 15x$

The graph was plotted using geogebra online graphing tool.

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