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: Identify the two - blue points

The two blue points are approximately $(30,30)$ and $(90,75)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $x_1 = 30,y_1 = 30,x_2=90,y_2 = 75$ into the formula: $m=\frac{75 - 30}{90 - 30}=\frac{45}{60}=\frac{3}{4}$.

Step3: Find the y - intercept $b$

Use the slope - intercept form $y=mx + b$ and substitute one of the points, say $(30,30)$ and $m=\frac{3}{4}$ into it. So $30=\frac{3}{4}\times30 + b$. Then $30=\frac{90}{4}+b$, and $b=30-\frac{90}{4}=\frac{120 - 90}{4}=\frac{30}{4}=\frac{15}{2}$.

Step4: Write the equation

The equation of the line in slope - intercept form is $y=\frac{3}{4}x+\frac{15}{2}$.

Answer:

$y=\frac{3}{4}x+\frac{15}{2}$