Write an equation in standard form for a line that is (a) parallel (b) perpendicular to the line with an equation of 3x - 5 that passes through the point (8, 5).

Answer 1

Hi Ley,

Your question should probably state: "to the line with an equation of y=3x-5" (slope-intercept form).

That said the slope of the original is m=3 (because of y = mx +b).

For a) parallel lines of equal slopes. So we know m=3 and a point P is given as P(8,5). That means we are ready to use point-slope: y - y₁ = m(x-x₁) where x₁= 8 and y₁=5.

So, y - 5 = 3(x-8). You can simplify that and put in slope-intercept form if you want.

For b) perpendicular lines have slopes that are negative reciprocals. So m = -1/3.

Giving y - 5 = -1/3 (x-8). Try getting used to using Desmos online graphing calculator to see how this works:

https://www.desmos.com/calculator/jvxarwgxqe

You can enable/disable the various equations to see that the graphs are the same.