Use algebra to find the point at which the line k ( x ) = − 2/3 x + 1/30 intersects the line h ( x ) = − 5/3 x − 13/6 .

Answer 1

Hi Sam - here’s a hint and the solution.

Hint: what does it mean when two lines intersect? Could you draw out an example? If you feel comfortable sketching out an example, how might you translate this into algebra?

Solution: if two lines k(x) and h(x) intersect, you can find the point of intersection by setting k(x) = h(x) and then solving for x. In algebraic terms,

k(x) = h(x)

=> -(2/3)x + 1/30 = -(5/3)x - 13/6

=> x = -11/5

Answer 2