write an equation for the line described: through (1,3) and perpendicular to the line through (-1,-1) and (2,0)

Question

geometry 

Answer 1

First, the slope formula to find the line's slope: (y2 - y1) / (x2 - x1)

^{0 - (-1)} / _{2 - (-1)}

m = ¹/₃

Now, a perpendicular line is going to be the negative inverse of the original line, so 1/3 becomes -3 for the new line

 

We have a slope, and we have a points, so we can use the point-slope formula:

y - y₁ = m(x - x₁)

y - 3 = -3(x - 1)

y - 3 = -3x + 3

Standard form: move the variables to one side and constants to the other:

3x + y = 6

Slope-intercept form: isolate y:

y = -3x + 6