Question

The scatter plot shows the relationship between the number of hours spent jogging and the number of minutes spent stretching, by the students on a track team:
A scatter plot is shown titled fitness routine. The x-axis is labeled hours jogging and the y-axis is labeled minutes stretching. Data points are located at 0 and 1, 2 and 1, 2 and 2, 4 and 3, 4 and 5, 6 and 3, 7 and 5, 9 and 4. A line connects the points 0 comma 1 and 10 comma 6.
What is the y-intercept of the line of best fit and what does it represent? (4 points)


1 minute; the number of minutes students stretch when they do not jog

1 hour; the number of hours students jog when they do not stretch

4 hours; the number of hours students jog when they do not stretch

4 minutes; the number of minutes students stretch when they do not jog


4.
(06.04)

The line of best fit for a scatter plot is shown:

A scatter plot and line of best fit are shown. Data points are located at 0 and 1, 2 and 1, 2 and 3, 4 and 3, 4 and 5, 6 and 3, 7 and 5, 9 and 4. A line of best fit passes through the y-axis at 1 and through the point 4 and 3.
What is the equation of this line of best fit in slope-intercept form? (4 points)


y = 1x + one half

y = one halfx + 1

y = 1x − one half

y = negative one halfx + 1


5.
(06.04)

The graph shows the number of cakes sold at Karen's Cake Shoppe for each of their 7 weeks in business:

A scatter plot is shown with the title Karens Cake Shoppe. The x axis is labeled Weeks in Business, and the y axis is labeled cakes sold. The data points are located at 1 and 2, 2 and 4, 3 and 5, 4 and 4, 5 and 6, 6 and 5, and 7 and 8. A line of best fit passes through the y axis at 1 and through the point 10 and 10.
If her current pattern continues, how many cakes will Karen most likely sell in her 10th week of business? (4 points)


10, because approximately y = 9 over 10.x + 1

11, because approximately y = 9 over 10.x + 1

8, because approximately y = 1x − 1

12, because approximately y = 1x + 2

Answer 1

The y-intercept of the first question is 1 and it represents the number of minutes they stretch when they don't jog.
#4) y=1/2x + 1
#5) 10 cakes, because y=9/10x+1

Explanation
For the first question:  The y-intercept is easily picked from the two points that define the line.  (0, 1) would have to be on the y-axis, because when we plot it, the x-coordinate is 0.  This means it is the y-intercept of the line.

#4) Finding the slope of the line, we use the formula 
m=(y₂-y₁)/(x₂-x₁) = (3-1)/(4-0) = 2/4 = 1/2

The y-intercept is at (0, 1), using the same justification as the first question.
This gives us the equation y = 1/2x + 1.

#5) First we find the equation of the line.  To do this, find the slope:
m=(y₂-y₁)/(x₂-x₁) = (10-1)/(10-0) = 9/10

The y-intercept is at (0, 1).  This makes our equation y=9/10x + 1.

Using 10 as x (x represents the number of weeks) we have
y=9/10(10) + 1
y=9/10(10/1) + 1
y=90/10 + 1
y=9+1 = 10