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.

Explanation:

Step1: Find the slope

The two blue points are $(20,10)$ and $(70,60)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
So, $m=\frac{60 - 10}{70 - 20}=\frac{50}{50}=\frac{5}{6}$.

Step2: Find the y - intercept

Using the slope - intercept form $y = mx + b$ and the point $(20,10)$.
Substitute $x = 20$, $y = 10$, and $m=\frac{5}{6}$ into $y=mx + b$.
$10=\frac{5}{6}\times20 + b$.
$10=\frac{100}{6}+b$.
$b = 10-\frac{100}{6}=\frac{60 - 100}{6}=0$.

Step3: Write the equation

Since $m=\frac{5}{6}$ and $b = 0$, the equation of the line in slope - intercept form is $y=\frac{5}{6}x+0$, which simplifies to $y=\frac{5}{6}x$.

Answer:

$y = \frac{5}{6}x$