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