Question

what is the equation in standard form of the line that passes through (4,13) and (8,5)? (hint: you have two points so run a regression. create the equation and then look at your answer choices! what do you need to do now?) x + 2y = 21 2x + y = 21 x + 3y = 21 3x - y = 21

Explanation:

Step1: Calculate the slope

The slope $m$ formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $(x_1,y_1)=(4,13)$ and $(x_2,y_2)=(8,5)$, then $m=\frac{5 - 13}{8 - 4}=\frac{-8}{4}=-2$.

Step2: Use point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(4,13)$ and $m=-2$, we have $y - 13=-2(x - 4)$.

Step3: Expand and convert to standard form

Expand: $y-13=-2x + 8$. Add $2x$ to both sides and add 13 to both sides. We get $2x+y=21$.

Answer:

B. $2x + y = 21$