Question

The scatter plot below shows the relationship between the leaf length (x) and leaf width f(x), in mm, of some leaves of a tree:ordered pairs 11, 0.5 and 12, 1 and 13, 1.5 and 14, 2 and 15, 2.5 and 16, 3 and 17, 3.5 and 18, 4 and 19, 4.5 and 20, 5 and 21, 5.5 and 22, 6Which of the following functions is best represented by the scatter plot?f(x) = −5 + 0.5xf(x) = 5 + 0.5xf(x) = x − 10.5f(x) = −x − 10.5

Answer 1

The best function represented by the scatter plot is f(x) = -5 + 0.5 x ⇒ 1st answer

Explanation:

* Lets talk about the scatter plot

- Scatter plots are similar to line graphs in that they use horizontal and

vertical axes to plot data points

- Scatter plots show how much one variable is affected by another.

- The relationship between two variables is called their correlation

- There are three types of correlation:

positive: one variable increases so the other increase

negative: as one variable increases, the other decreases

no correlation: there is no clear relationship between the variables

* Lets solve the problem

- The scatter plot shows the relationship between the leaf length (x)

and leaf width f(x)

- Some leaves of a tree are ordered pairs:

# (11 , 0.5) , (12 , 1) , (13 , 1.5) , (14 , 2) , (15 , 2.5) , (16 , 3) , (17 , 3.5) ,

(18 , 4) , (19 , 4.5) , (20 , 5) , (21 , 5.5) , (22 , 6)

∵ The scatter plot is similar to the line graph

- Lets find the equation which represents the relation between

x and f(x)

∵ The form of the linear equation is y = mx + c, where m is the slope

of the line and c is the y-intercept

- The rule of the slope of the line which passes through points (x1 , y1)

and (x2 , y2) is:
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

- Chose any two points to find the slope of the line

∵ (12 , 1) and (14 , 2) are two points on the line

∴
`m=(2-1)/(14-12)=(1)/(2)=0.5`

- Substitute the value of m in the equation

∴ y = 0.5 x + c

- To find c use any point from above and substitute x and y by its

coordinates

∵ Point (16 , 3) lies on the line

∴ 3 = 0.5(16) + c ⇒ simplify

∴ 3 = 8 + c ⇒ subtract 8 from both sides

∴ 3 - 8 = c

∴ c = -5

- Substitute the value of c in the equation

∴ y = 0.5 x - 5

* The best function represented by the scatter plot is f(x) = -5 + 0.5 x