Question

what is the equation of the trend line in the scatter plot?
use the two blue points to write the equation in slope - intercept form. write any coefficients as integers, proper fractions, or improper fractions in simplest form.
image img
options:
y = 50/80x + 40
y = 50/80x - 40
y = 5/8x + 40
y = 5/8x + 40

Explanation:

Step1: Identify the two blue points

From the scatter plot, the two blue points are \((0, 40)\) (the y - intercept) and \((80, 90)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,40)\) and \((x_2,y_2)=(80,90)\). Then \(m=\frac{90 - 40}{80 - 0}=\frac{50}{80}=\frac{5}{8}\).

Step3: Write the equation in slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m=\frac{5}{8}\) and \(b = 40\) (since the line crosses the y - axis at \((0,40)\)). So the equation of the line is \(y=\frac{5}{8}x + 40\).

Answer:

\(y=\frac{5}{8}x + 40\)