Question

what is the equation of the trend line in the scatter plot?
use the two orange points to write the equation in slope - intercept form. write any coefficients as integers, proper fractions, or improper fractions in simplest form.

Explanation:

Step1: Identify the two orange points

From the scatter plot, the two orange points are \((40, 0)\) and \((90, 70)\).

Step2: Calculate the slope (\(m\))

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(40,0)\) and \((x_2,y_2)=(90,70)\). Then \(m=\frac{70 - 0}{90 - 40}=\frac{70}{50}=\frac{7}{5}\).

Step3: Find the y - intercept (\(b\))

Use the slope - intercept form \(y = mx + b\) and one of the points, say \((40,0)\). Substitute \(x = 40\), \(y = 0\) and \(m=\frac{7}{5}\) into the equation:
\(0=\frac{7}{5}(40)+b\)
\(0 = 56 + b\)
Subtract 56 from both sides: \(b=- 56\).

Step4: Write the equation

The slope - intercept form is \(y=mx + b\). Substitute \(m = \frac{7}{5}\) and \(b=-56\) into the formula: \(y=\frac{7}{5}x-56\).

Answer:

\(y=\frac{7}{5}x - 56\)