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Every week Ben collects a few pounds of paper to recycle. The graph below shows the total number of pounds of paper (y) that Ben collected in a certain amount of time (x), in weeks:


A graph titled Paper Recycling is shown with labels in x axis and y axis as Number of Weeks and Amount of Paper Collected in pounds, respectively. The values on the x axis are from 0 to 5 at increments of 1, and the values on the y axis are from 0 to 150 at increments of 30.


Dots are made at 0, 30 and 1, 60 and 2, 90 and 3, 120 and 4, 150. A straight line joins 0, 30 and 4,150. What would most likely be the total amount of paper, in pounds,


Ben would collect in 10 weeks?

230

270

300

330

Respuesta :

kudzordzifrancis
Since the graph is a straight line, its equation is of the form;

[tex]y = mx + c[/tex]
Where m is the slope and c is the y intercept

We can use any two points on the straight line to find the value of m and c.

Let us use (0,30) and (4,150)

[tex]m = \frac{150 - 30}{4 - 0} [/tex]
This simplifies to,

[tex]m = \frac{120}{4} = 30[/tex]
Let us substitute the value of m to obtain,

[tex]y = 30x + c[/tex]
Substitute any of the points to find c. It is easier to use (0,30).

[tex]30 = 30(0) + c[/tex]
[tex]c = 30[/tex]
The equation of the graph now becomes,

[tex]y = 30x + 30[/tex]
So in 10 weeks Ben will collect,

[tex]y = 30(10) + 30[/tex]
[tex]y = 300 + 30[/tex]
[tex]y = 330[/tex]
Ben will collect 330 papers.


You can also use any two points to find the equation of this line.
anthonymachado0407

Answer: 330 pounds of paper

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