a line of best fit was drawn to the plotted points in a data set below. based on the line of best fit, for…

a line of best fit was drawn to the plotted points in a data set below. based on the line of best fit, for what x - value does $y = 13$?

a line of best fit was drawn to the plotted points in a data set below. based on the line of best fit, for what x - value does $y = 13$?

Answer

Explanation:

Step1: Find the slope of the line

The formula for slope (m=\frac{y_2 - y_1}{x_2 - x_1}). Using points ((0,4)) and ((8,10)), we have (m=\frac{10 - 4}{8 - 0}=\frac{6}{8}=\frac{3}{4}).

Step2: Write the equation of the line

The slope - intercept form of a line is (y=mx + b). Since (b = 4) (the (y) - intercept when (x = 0)) and (m=\frac{3}{4}), the equation is (y=\frac{3}{4}x+4).

Step3: Solve for (x) when (y = 13)

Substitute (y = 13) into the equation (13=\frac{3}{4}x+4). First, subtract 4 from both sides: (13 - 4=\frac{3}{4}x), so (9=\frac{3}{4}x). Then, multiply both sides by (\frac{4}{3}): (x=9\times\frac{4}{3}=12).

Answer:

(x = 12)