Two lines are formed from the following pairs of points: • through and • through and

MATHEMATICS · Multi-part · AoPS · Mathematics · Lines Graphing · Lines Graphing

Problem

Two lines are formed from the following pairs of points: •

L_1

through

(4,3)

and

(4,-5)

•

L_2

through

(-2,6)

and

(5,6)

(i) Write the equation of

L_1

and of

L_2

in their simplest algebraic forms. (ii) Comment on the nature of the slopes of

L_1

and

L_2

. (iii) Find the coordinates of the point where

L_1

and

L_2

intersect. (iv) Determine the equation of the straight line passing through the origin and the intersection point found in part (iii).