MATH SOLVE

4 months ago

Q:
# 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 + 0.5x f(x) = 5 + 0.5x f(x) = x − 10.5 f(x) = −x − 10.5

Accepted Solution

A:

Answer:The best function represented by the scatter plot is f(x) = -5 + 0.5 x ⇒ 1st answerStep-by-step 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: [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]- Chose any two points to find the slope of the line∵ (12 , 1) and (14 , 2) are two points on the line∴ [tex]m=\frac{2-1}{14-12}=\frac{1}{2}=0.5[/tex]- 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