Question

Carl 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 and scale along y axis from 0 to 15 at increments of 1. The ordered pairs 0, 1 and 1, 2.5 and 2, 3.8 and 3, 6 and 4, 5 and 5, 8 and 6, 10 and 7, 11 and 8, 13 and 9, 13.5 and 10, 15 are shown on the graph. A straight line joins the ordered pairs 0, 1 and 10, 15. What is the approximate equation of this line of best fit in slope-intercept form? (1 point)
y = x + 7 over 5
y = 7 over 5x + 1
y = 5 over 7x + 1
y = x + 5 over 7

Answer 1

Option B: $y=\frac{7}{5} x+1$ is the line of best fit in slope - intercept form

Explanation:

It is given that the straight line joins the ordered pairs $(0,1)$ and $(10,15)$

We need to determine the line of best fit in slope - intercept form.

The equation of the line of best fit in slope - intercept form is given by

$y=mx+b$

where m is the slope and b is the y - intercept

The slope can be determined by substituting the points $(0,1)$ and $(10,15)$ in the formula,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{15-1}{10-0}$

$m=\frac{14}{10}$

$m=\frac{7}{5}$

Thus, the slope is $m=\frac{7}{5}$

The y - intercept is the value of y when the value of the x - coordinate is zero.

Thus, from the ordered pair $(0,1)$ , the y -intercept of the graph is $b=1$

Substituting the slope and the y - intercept in the equation $y=mx+b$, we get,

$y=\frac{7}{5} x+1$

Thus, the equation of line of best fit in slope - intercept form is $y=\frac{7}{5} x+1$

Hence, Option B is the correct answer.