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. y=

Explanation:

Step1: Identify the two - point coordinates

The two blue points are $(30,10)$ and $(70,60)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $(x_1,y_1)=(30,10)$ and $(x_2,y_2)=(70,60)$ into the formula: $m=\frac{60 - 10}{70 - 30}=\frac{50}{40}=\frac{5}{4}$.

Step3: Use the point - slope form to find the y - intercept $b$

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(30,10)$ and $m = \frac{5}{4}$, we have $y-10=\frac{5}{4}(x - 30)$. Expand it: $y-10=\frac{5}{4}x-\frac{150}{4}$. Then $y=\frac{5}{4}x-\frac{150}{4}+10$. Since $10=\frac{40}{4}$, we get $y=\frac{5}{4}x-\frac{150 - 40}{4}=\frac{5}{4}x-\frac{110}{4}=\frac{5}{4}x-\frac{55}{2}$.

Answer:

$y=\frac{5}{4}x-\frac{55}{2}$