Pat created a scatter plot and drew a line of best fit, as shown.

What is the equation of the line of best fit that Pat drew?

Work Shown:

We will only focus on the two points that are on the regression line.

Those two points are (10,5) and (15,4)

Let (x1,y1) = (10,5) and (x2,y2) = (15,4)

Find the slope of the line through (x1,y1) = (10,5) and (x2,y2) = (15,4)

m = (y2 - y1)/(x2 - x1)

m = (4 - 5)/(15 - 10)

m = -1/5

m = -0.2

Plug m = -0.2, and  (x1,y1) = (10,5) into the point slope formula. Solve for y

y - y1 = m(x - x1)

y - 5 = -0.2(x - 10)

y - 5 = -0.2*x - 0.2*(-10) ... distribute

y - 5 = -0.2*x + 2

y - 5+5 = -0.2*x + 2 + 5 ... add 5 to both sides

y = -0.2*x + 7

y = (-1/5)*x + 7 convert -0.2 to -1/5

The equation y = (-1/5)x + 7 is in the form y = mx+b with m = -1/5 = -0.2 as the slope and b = 7 as the y intercept. The y intercept is where the graph crosses the vertical y axis. More specifically, the location of the y intercept in this case is at the point (0,7).

step-by-step explanation:

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c