lines and equations

Question

Write the equation of a line that is perpendicular to the given line and that passes through the given point.

y = x ; (–4, 2)

Answer 1

The ungarbled equation is y = x and the point is (-4, 2)

The equation of the line perpendicular is y = -x + b.

2 = -4 + b

6 = b

y = -x + 6

Answer 2

Going by what's visible in the title, it seems you are asked to find the equation of a line that runs through (-4,2) and is perpendicular to y = x.

Well, what does the equation of a line look like?

y = mx + b, with m being the slope and b being the y-intercept. Of course, there is no m or b in our equation!

Buuuuuut, remember we don't call you 1 Desi, right? That would be silly. We just call you Desi and that means there's one of you, so x really means 1x, meaning m = 1.

What about b?? We also don't say, "There's Desi and no one else" when you are alone; it's implied. With no b shown, it's implied that b = 0, but again, we don't just add 0 to things all willy nilly.

Now, we have two choices. Remember that perpendicular lines have opposite, reciprocal slopes. Since 1 = 1/1, the opposite reciprocal is -1/1, which is just -1.

1. y - y₁ = m(x - x₁)

y - 2 = -1(x - (-4))

y - 2 = -x - 4

y = -x - 2

2. y = mx + b

2 = -1(-4) + b

2 = 4 + b

b = -2

y = -x - 2

Let's check.

2 = -(-4) - 2

2 = 4 - 2

2 = 2

0 = 0

Hey, look at that!