Question

A graph shows the survey results for a group of students who were asked how many honors classes they have taken and how many elective classes: A scatter plot is shown with the title class choices. The x axis is labeled number of honors classes and the y axis is labeled number of electives. Data points are located at 1 and 8, 3 and 6, 3 and 9, 5 and 3, 6 and 6, 6 and 9, 8 and 6. A line of best fit crosses the y axis at 9 and passes through the point 6 and 6. How many elective classes would students likely have taken if they have taken 12 honors classes? 15, because y = one halfx + 9 12, because y = y = negative one halfx + 9 6, y = ˜one halfx + 9 3, because y = negative one halfx + 9

Answer 1

Option D.

Explanation:

It is given that a line of best fit crosses the y axis at 9 and passes through the point (6,6).

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The line passes through (0,9) and (6,6). So, the equation of line is

`y-9=(6-9)/(6-0)(x-0)`

`y-9=-(1)/(2)(x)`

Add 9 from both sides.

`y=-(1)/(2)(x)+9`

The equation of best fit line is
`y=-(1)/(2)(x)+9`.

Substitute x=12 in the above equation.

`y=-(1)/(2)(12)+9`

`y=-6+9`

`y=3`

3 elective classes would students likely have taken if they have taken 12 honors classes.

Therefore, the correct option is D.

Answer 2

The first thing to do in this case is to find the equation of the line that represents the problem.
You have two points given:
(0, 9)
(6, 6)
The generic equation is:
y-yo = m (x-xo)
Where;
m = (y2-y1) / (x2-x1)
m = (6-9) / (6-0)
m = -3 / 6
m = -1 / 2
We choose any point:
(xo, yo) = (0, 9)
We rewrite:
y-yo = m (x-xo)
y-9 = (- 1/2) (x-0)
y = -1 / 2x + 9
So we have that for x = 12
y = -1 / 2 (12) +9
y = -6 + 9
y = 3
answer:
3, because y = negative one halfx + 9