Question

find the point - slope equation for the line that passes through the points (1, 4) and (2, 6). use the first point in your equation. y - ? = (x - )

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, $x_1 = 1,y_1 = 4,x_2=2,y_2 = 6$. So, $m=\frac{6 - 4}{2 - 1}=\frac{2}{1}=2$.

Step2: Write the point - slope equation

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the first point $(1,4)$ and $m = 2$, we substitute $y_1 = 4$ and $x_1 = 1$ into the equation.

Answer:

$y - 4=2(x - 1)$