To find the equationof a line that passes through 2 given points, we use the following steps:
1 - given point (x1, y1) and (x2, y2), find the slope "s":
[tex]s=\frac{y_2-y_1}{x_2-x_1}[/tex]
2 - Using the slope and one of the given points, write the equation in the slope-point form:
[tex](y-y_1)=s(x-x_1)[/tex]
3 - Solve fo "y" to get the slope-intercept form as an answer.
So:
1 - Find the slope:
[tex]s=\frac{4-6}{5-1}=\frac{-2}{4}=-\frac{1}{2}[/tex]
2 - Write the slope-point form:
[tex](y-6)=-\frac{1}{2}(x-1)[/tex]
3 - Solve for y:
[tex]\begin{gathered} y-6=-\frac{1}{2}x+\frac{1}{2} \\ y=-\frac{1}{2}x+\frac{1}{2}+6 \\ y=-\frac{1}{2}x+\frac{1+12}{2} \\ y=-\frac{1}{2}x+\frac{13}{2} \end{gathered}[/tex]
So, the equation of the line is:
[tex]y=-\frac{1}{2}x+\frac{13}{2}[/tex]
