Answer:
An equation of the line that passes through the points (6, -6) and (-6, -8) is [tex]\mathbf{y+6= \frac{1}{6}(x-6)}[/tex]
Step-by-step explanation:
We need to write an equation of the line that passes through the points (6, -6) and (-6, -8)
We would use point slope formula: [tex]y-y_1=m(x-x_1)[/tex]
where [tex]x_1=6, y_1=-6 \ and \ m \ is \ slope[/tex]
Finding slope using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\[/tex]
We have [tex]x_1=6, y_1=-6, x_2=-6, y_2=-8[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\\\Slope=\frac{-8-(-6)}{-6-6}\\Slope=\frac{-8+6}{-12}\\Slope=\frac{-2}{-12}\\Slope=\frac{1}{6}[/tex]
So, slope = 1/6
The required equation having [tex]x_1=6, y_1=-6 \ and \ m =\frac{1}{6}[/tex]
[tex]y-(-6)=\frac{1}{6}(x-6)\\y+6= \frac{1}{6}(x-6)[/tex]
An equation of the line that passes through the points (6, -6) and (-6, -8) is [tex]\mathbf{y+6= \frac{1}{6}(x-6)}[/tex]
