Question

a regression line contains the point (21.02, 35.5). the slope of the regression line is approximately 3.1. what is the equation of the regression line? a y = 3.1x - 35.5 b y = 3.1x + 35.5 c y = 3.1x - 29.00 d y = 3.1x + 21.02

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1 = 21.02$, $y_1=35.5$ and $m = 3.1$.

Step2: Substitute values into point - slope form

Substitute the values into the formula:
$y-35.5 = 3.1(x - 21.02)$

Step3: Expand the right - hand side

Using the distributive property $a(b - c)=ab - ac$, we have:
$y-35.5=3.1x-3.1\times21.02$
Calculate $3.1\times21.02$: $3.1\times21.02 = 3.1\times(21 + 0.02)=3.1\times21+3.1\times0.02=65.1+0.062 = 65.162$
So, $y-35.5 = 3.1x-65.162$

Step4: Solve for y

Add 35.5 to both sides of the equation:
$y=3.1x-65.162 + 35.5$
Calculate $-65.162+35.5=-29.662\approx - 29.00$ (approximate value)
So the equation of the line is $y = 3.1x-29.00$

Answer:

C. $y = 3.1x-29.00$