29.5k views
3 votes
"Activity: Graphing a Nonproportional Line

This activity is designed to help you achieve various educational goals related to mathematical practices, problem-solving, and understanding real-world situations. You will work with the equation derived in the first Lesson Activity, which models a car wash: y = 5x - 75.

Is it possible to graph the line that represents this equation by using two points found in the previous Lesson Activity, namely (15, 0) and (0, -75)? Please explain your answer."

User Relandom
by
7.9k points

1 Answer

6 votes

Final answer:

It is possible to graph the line using the points (15, 0) and (0, -75), with the latter being the y-intercept and the former indicating a point where the y-value becomes zero. Together they provide a visual representation of the nonproportional relationship depicted by the car wash equation, y = 5x - 75.

Step-by-step explanation:

Yes, it is possible to graph the line that represents the equation y = 5x - 75 by using the two points (15, 0) and (0, -75). To graph a line accurately, you only need two points through which the line passes.

These points are sufficient to establish the position and slope of the line.

The point (0, -75) is known as the y-intercept because it is where the line crosses the y-axis.

The other point, (15, 0), indicates that after a certain value on the x-axis, specifically 15 units, the y-value of the line becomes zero.

Together, these points help us plot the line: start by marking the y-intercept at (0, -75) on the graph, then move to the second point at (15, 0) and draw a straight line through these two points.

This will give you the graph of the line representing the car wash equation.

Reading graphs is essential in understanding economic relationships, and a straight line graph can illustrate such relationships clearly. In this case, the equation y = 5x - 75 displays a nonproportional relationship because of the presence of the y-intercept (-75).

Hence, the slope, which is the coefficient of x (in this case, 5), confirms that for each unit increase in x, y increases by 5 units, until the cost is covered by reaching the break-even point at (15, 0).

User Lita
by
8.0k points