Question

write equation of the line containing (3,2) and (4,4)
y = 2x - 4
y = 1/2x + 2
y = -2x + 12
y = 1/2x + 4 1/2

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(3,2)$ and $(x_2,y_2)=(4,4)$. So $m=\frac{4 - 2}{4 - 3}=\frac{2}{1}=2$.

Step2: Use the point - slope form

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

Step3: Simplify the equation

Expand the right - hand side: $y - 2=2x-6$. Then add 2 to both sides to get $y=2x - 4$.

Answer:

A. $y = 2x-4$