Question

The graph below shows the relationship between the number of months different students practiced tennis and the number of matches they won:

Part A: What is the approximate y-intercept of the line of best fit and what does it represent?

Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope.

Answer 1

1 is 3 and 2 is y 2/1x

Answer 2

Part A : y-intercept is approximately 3.25

Part B : equation of the line is

`y=(7)/(4)x+(13)/(4)`

Slope is
`(7)/(4)`

The number of matches would be 26 after 13 months of practice.

Explanation:

By the given diagram,

The line is passes through the points (1, 5) and (5,12),

∵ equation of a line passes through the point
`(x_1,y_1)` and
`(x_2,y_2)` is,

`y-y_1=(x_2-x_1)/(y_2-y_1)(x-x_1)`

Thus, the equation of the line would be,

`y-5=(12-5)/(5-1)(x-1)`

`y-5=(7)/(4)(x-1)`

`y-5=(7x)/(4)-(7)/(4)`

`y=(7)/(4)x-(7)/(4)+5\implies y=(7x)/(4)+(13)/(4)`

Part A : Now, if x = 0,

`\implies y=(13)/(4)\approx 3.25`

Hence, the y-intercept of the line would be approx 3.25,

Part B:

The slope intercept form of a line is,

y = mx + c

Where, m is the slope,

Hence, the slope intercept form of the line is,

`y=(7)/(4)x+(13)/(4)`

Having slope
`(7)/(4)`

If x = 13,

`y=(7)/(4)(13)+(13)/(4)= (91)/(4)+(13)/(4)=(104)/(4)=26`

Therefore, the number of matches would be 26 after 13 months of practice.