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

The y intercept should represent how much matches the team won without practice

Here its 3

• (0,3)

#2

• (0,3)
• (5,12)

Slope

• m=12-3/5
• m=9/5

Equation in point slope form

• y-3=9/5x
• y=9/5x+3

After 13 months

• y=9/5(13)+3=117/5+3

Approximately 26matches

Answer 2

(a) (i) y-intercept = 3

(ii) Represents that the team won 3 matches without any practice.

(b) (i) Equation: y = 1.8x + 3,

(ii) 26 matches won

The approximate y-intercept can be determined by seeing when the best fit line crosses the y axis.

Part A

Here the best line crosses the y-axis when y = 3. So coordinates: (0, 3)

Part B

Take two best points touching the line: (0,3), (5, 12)

`\sf slope \ (m) = (y_2 - y_1)/(x_2 - x_1) = (12-3)/(5-0) = 1.8`

Equation:

y - y₁ = m(x - x₁)

y - 3 = 1.8(x - 0)

y = 1.8x + 3

So, after 13 months of practice: y = 1.8(13) + 3 = 26.4 ≈ 26 matches won.