Gcse Maths Exam Question

Question:

The equation of the line L₁ is y = 3x 2. The equation of the line L₂ is 3y 9x + 5 = 0. Show that these two lines are parallel.

Solution:The equation of a line is y = mx + c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient.

L₁ has equation y = 3x 2, so the gradient is 3.

In order to find the gradient of L₂ we must rearrange the equation so that it is in the form y = mx + c.

3y 9x + 5 = 0

(+9x and -5 to each side of the equation)

3y = 9x 5

(Divide each term by 3)

y = 3x - 5/3

Therefore, the gradient of L₂ is 3.

Since L₁ and L₂ both have gradients of 3, they are parallel lines.