The equation of a line that passes through two points [tex](x_1, \, y_1)[/tex] and [tex](x_2, \, y_2)[/tex] is given by
[tex] \frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1} [/tex]
Give a line that passes through the points (6, 10) and (12, 7), the equation of the line is obtained as follows:
[tex]\frac{y-10}{x-6} = \frac{7-10}{12-6}= \frac{-3}{6} =- \frac{1}{2} \\ \\ 2(y-10)=-(x-6) \\ \\ 2y-20=-x+6 \\ \\ 2y=-x+26 \\ \\ y=- \frac{1}{2} x+13[/tex]
The equation of a line in slope intercept form is given by
[tex]y=mx+c[/tex]
where: m is the slope and c is the y-intercept.
Comparing this with the obtained equation of the line that passes through the points (6, 10) and (12, 7), we notice that the line has a slope of [tex]- \frac{1}{2}[/tex] and a y-intercept of 13.
