Question

Shannon drew the line of best fit on the scatter plot shown below:

A graph is shown with scale along x axis from 0 to 10 at increments of 1 and scale along y axis from 0 to 15 at increments of 1.The ordered pairs 0, 14 and 1, 13.1 and 2, 12 and 3, 10 and 4, 8.5 and 5, 7 and 5.6, 6 and 6, 4.9 and 7, 3.4 and 8, 2.9 and 9, 2 and 9.5, 0.5 are shown on the graph. A straight line joins the ordered pairs 0,14 and 10, 0.

What is the approximate equation of this line of best fit in slope-intercept form?
y = negative 7 over 5x + 14
y = −14x + 7 over 5
y = negative 5 over 7x + 14
y = −14x + 5 over 7

Answer 1

Using the points (0,14) and (10,0), the gradient of the line is (14-0)/(0-5) which simplifies to -7/5.

From these points, we can also see that when the x value is zero, the y value is 14. Therefore the y-intercept is 14.

We can then put this into the equation of a straight line, y=mx+c:

y = (-7/5)x + 14

Answer 2

Option A.

Explanation:

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)`

It is given that the line of best fit passes through the points (0,14) and (10,0).

Using the above formula the equation of best fit line is

`y-14=(0-14)/(10-0)(x-0)`

`y-14=(-14)/(10)(x)`

`y-14=-(7)/(5)(x)`

Add 14 on both sides.

`y-14+14=-(7)/(5)(x)+14`

`y=-(7)/(5)(x)+14`

The equation of best fit line is
`y=-(7)/(5)(x)+14`.

Therefore, the correct option is A.