Question

Find the equation of given points. Write the equation in slope-intercept form. (2,5)(6,1)

Answer 1

Equation of a line in slope-intercept form

$y=mx+b$

where m is the slope and b is the y-intercept.

The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:

$m=\frac{y_2-y_1}{x_2-x_1}$

This line passes through (2,5) and (6,1), then its slope is:

$m=\frac{1-5}{6-2}=\frac{-4}{4}=-1$

Substituting with the point (2, 5) and m = -1 into the general equation and solving for b:

$\begin{gathered} 5=\lparen-1)\cdot2+b \\ 5=-2+b \\ 5+2=b \\ 7=b \end{gathered}$

Substituting with m = -1 and b = 7 into the general equation, the equation of this line is:

$y=-x+7$