Question

(06.04 MC) Dennis 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, 15 and 0.5, 14 and 1, 13 and 2, 12 and 3, 11 and 4, 9 and 5, 8 and 6, 6 and 7, 4.5 and 8, 2.3 and 9, 2 and 9.8, 0.5 are shown on the graph. A straight line joins the ordered pairs 0, 15 and 10, 0. What is the approximate equation of this line of best fit in slope-intercept form?

Answer 1

Answer:

The approximate equation of this line of best fit in slope-intercept form is $y=-\frac{3}{2}x+15$.

Step-by-step explanation:

The point slope form of a line is

$y=mx+b$

Where, m is slope and b is y intercept.

If a line passing through two points then the slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}$

It is given that the straight line of best fit joins the ordered pairs (0, 15) and (10, 0). So, the y-intercept is 15 and the slope of the line is

$m=\frac{0-15}{10-0}=-\frac{3}{2}$

The y-intercept is 15 and the slope of the line is $-\frac{3}{2}$, therefore the approximate equation of this line of best fit in slope-intercept form is

$y=-\frac{3}{2}x+15$

Answer 2

Using the two points on the line:

(0,15) and (10,0)

The slope of the line is the change in Y over the change in x:

slope = 0 -15 / 10-0

Slope = -15/10 , Dividing by 5 this can be reduced to -3/2

The y-intercept is the y value, when x equals 0, in this problem they give you the point (0,15), which means Y is 15 when x is 0.

The equation of a line is written as y = mx+b, wherem is the slope and b is the y-intercept.

Replace m and b with the calculated slope and y-intercept to get:

y = -3/2x + 15