Question

What is the equation of the line that passes through the points (–p, –q) and (p, q)?

Answer 1

Answer:

$y=\frac{q}{p}x$

Step-by-step explanation:

First we find the slope.  The formula for slope is

$m=\frac{y_2-y_1}{x_2-x_1}$

Using our two points, we have

m = (q--q)/(p--p) = (q+q)/(p+p) = 2q/2p = q/p

Point-slope form of an equation is

$y-y_1=m(x-x_1)$

Using the first point as (x₁, y₁) and our value for m, we have

y - -q = (q/p)(x - - p)

y + q = (q/p)(x + p)

Using the distributive property, we have

y + q = (q/p)x + (q/p)p

y + q = (q/p)x + (q/p)(p/1)

y + q = (q/p)x + qp/p

y + q = (q/p)x + q

Subtract q from each side:

y + q - q = (q/p)x + q - q

y = (q/p)x

Answer 2

slope (y2-y1)/(x2-x1)

m = (q--q)(p--p)

m = 2q/2p

m=q/p

point slope form

y-y1=m(x-x1)

y-q =q/p(x-p)

distribute

y-q=q/p *x -q

add q to each side

y = q/p *x