Given:
Number of hours spent studying
(x) 0 0.5 1 1.5 2 2.5 3 3.5 4
Score on the music test
(y) 60 62 64 66 68 70 72 74 76
Required:
We need to find the function that best fits the data and slope and y-intercept of the plot.
Explanation:
B)
Recall that a line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.
Here best-fit equation is a line that passes through all given points.
Consider the line equation.
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
Consider the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Consider points (0,60) and (1,64).
[tex]Substitute\text{ }y_2=64,y_1=60,x_2=1,\text{ and }x_1=0\text{ in the formula.}[/tex][tex]m=\frac{64-60}{1-0}[/tex][tex]m=4[/tex]Recall that the y-intercept point is the intersection point where the line meets the y-axis.
The point (0,60) is the intersection point where the line meets the y-axis.
[tex]b=60[/tex]Substitute m=4 and b =60 in the line equation.
[tex]y=4x+60[/tex]The function that best fits the data is y =4x+60.
C)
The slope of the plot indicates scores on the music test increased by 4 per one hour of studying.
The y-intercept of the plot indicates the score on the music test is 60 when they do not study.
