Question

what is the equation in standard form of the line that passes through the points (3, 12) and (7, 4)?
2x - y = 18
x + 2y = 18
x - 2y = 18
2x + y = 18

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)=(3,12)$ and $(x_2,y_2)=(7,4)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 12}{7 - 3}=\frac{-8}{4}=-2$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(3,12)$ and $m = - 2$, we have $y - 12=-2(x - 3)$.

Step3: Expand and convert to standard form

Expand the point - slope equation: $y-12=-2x + 6$. Then, move all terms to one side to get the standard form $Ax+By = C$. Add $2x$ to both sides and add 12 to both sides: $2x+y=18$.

Answer:

D. $2x + y = 18$