Question

Caleb is studying for his end-of-year exams. The graph below shows the number of hours he studied for the first six days. A line of best fit has been drawn on the graph.

Scatter plot with line of best fit in the first quadrant titled Calebs Studying Time, shows Day on the x axis and Number of Hours Studied on the y axis. The x axis scale is from 0 to 8 in increments of 1. The y axis scale is from 0 to 7 in increments of 1. The line of best fit passes through the points one comma one and four comma two.

Based on the line of best fit, for how many hours will Caleb study on day 10?

Answer 1

Well, you need to know the y coordinate when x=10. A couple of ways to go about this.

The more technical way would be to find the equation for the line. You have 2 points, so you can use them to find the equation (first find slope, then use slope and one point to find the equation for the line). Once you have that, just plug in x=10 and see what you get.

The less formal (but still effective) way is just to look at the ratios between the coordinates of the points, and see if you can determine what y will be when x=10

You have (1, 1) and (4, 2)

So each time you increase x by 3, you increase y by 1.

So from x=4 to x=10, you need to increase x by 6. So y will increase by....??

So y=? when x=10?

Answer 2

i got 5?

Answer 3

How? Show your reasoning.

Answer 4

an increase of +3 in x means an increase of +1 in y.

So from (4, 2) you go to x=7 and y=2+1=3

Now, from (7, 3) you go to x=? and y =?

Answer 5

4?

Answer 6

Yes.

Answer 7

thank you