Question

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

The title of the graph is Tennis Matches. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Matches Won. The scale on the y axis is from 0 to 22 at increments of 2, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 2 and 1, 5 and 2, 8 and 3, 9 and 4, 10 and 5, 12 and 6, 13 and 7, 16 and 8,17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 3.3 and 2, 6.8 and 4, 10 and 6, 13.5 and 8, 17 and 10, 20.5.

Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)

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. (5 points)

Answer 1

See below ~

Step-by-step explanation:

Part A :

• The approximate y-intercept of the line is about (0, 3)
• This represents that with 0 months of practice, 3 matches are won

Part B :

• Finding the slope
• Take two points on the line : (0, 3) and (5, 12)
• m = y₂ - y₁ / x₂ - x₁
• m = 12 - 3 / 5 - 0
• m = 9/5
• m = 1.8 (slope)

Forming the equation :

• y = mx + b (where m is the slope and b is the y-intercept)
• y = 1.8x + 3

Predicting how many matches can be won with 13 months of practice :

• Here, x (number of months) = 13
• y = 1.8(13) + 3
• y = 23.4 + 3
• y = 26.4
• y = 26 matches (roughly)

Answer 2

Step-by-step explanation:

Part A

y-intercept: 3

It represents that after 0 months practice, the number of matches won is 3.

Part B

slope intercept form: y = mx + b

Here to find slope,

take two points: (5, 12), (0, 3)

`\sf slope: (y_2-y_1)/(x_2-x_1) = (rise)/(run)`

`\rightarrow \sf slope = (3-12)/(0-5) = 1.8`

Equation:

y - y1 = m(x- x1)

y - 12 = 1.8(x - 5)

y = 1.8x - 9 + 12

y = 1.8x + 3

To find Matches won after 13 months

insert x = 13

y = 1.8(13) + 3

y = 26.4 ≈ 26 matches

The team could have won 26 matches after 13 months practice.