Question

The graph shows Linda's math scores versus the number of hours spent doing math homework.

What will most likely be Linda's approximate math score if she does math homework for 7 hours a week?

A. 62.5 Points

B.77.5 Points

C. 82.5 Points

D.93.5 Points

Answer 1

Answer=A

Let's write the an equation in slope intercept for for the line.

y-intercept=10

slope=rise/run=15/2=7.5

equation:

y=mx+b
y=7.5x+10

Solve for x=7

y=7.5(7)+10
y=52.5+10
y=62.5

Answer=A

Answer 2

The approximate score is:

Option: A

A. 62.5 points.

Explanation:

Clearly from the graph we could observe that the line of best fit passes through (0,10) and (4.5,45).

Now we find the equation of line of best fit with the help of formula that is used to find the equation of a line passing through (a,b) and (c,d) as:

`y-b=(d-b)/(c-a)* (x-a)`

Here we have:

(a.,b)=(0,10) and (c,d)=(4.5,45)

Hence, the line of best fit is given as:

`y-10=(45-10)/(4.5-0)*(x-0)\\\\y-10=(35)/(4.5)* x\\\\y-10=(70)/(9)* x\\\\y=(70)/(9)* x+10`

Now we are asked to find the math score if she does math homework for 7 hours a week i.e. we have to find the value of y when x=7.

Hence, we put x=7 in the equation to obtain y as:

`y=(70)/(9)* 7+10\\\\y=(490)/(9)+10\\\\y=64.44`

Hence, the approximate score is:

Option: A

A. 62.5 points.