Question

QuestionDetermine the equation of the line passing through the points (3, 1) and (5, -1).Write the linear equation in slope-intercept formy = mx +b.

Answer 1

Given the points (3, 1) and (5, -1)

we will write the equation of the line using the slope-intercept form:

$y=mx+b$

Where (m) is the slope and (b) is the y-intercept

The slope will be calculated as follows:

$\begin{gathered} slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{-1-1}{5-3}=\frac{-2}{2}=-1 \end{gathered}$

substitute with m into the equation of the line:

$y=-x+b$

Substitute with point (3, 1) to find the value of (b)

$\begin{gathered} 1=-3+b \\ b=1+3=4 \end{gathered}$

Substitute with (m) and (b) into the equation of the line

So, the answer will be:

$y=-x+4$