Equation of the line

Question

Write the equation of the line that passes through the point (20,-3) and is parallel to

Answer 1

Given any equation of a line, rearrange it (if necessary) to fit the standard form y = mx + b

m is gradient, b is y intercept i.e. point on line is (0,b)

e.g. y = 2x + 1 is in this form, m=2, b=1

e.g. 2x = 3y + 1 needs rearranging => 3y = 2x - 1 => y = ²/₃ x - ¹/₃

So now you have the gradient of your given line.

Property of parallel lines is that they have the same gradient.

If our line is 2x = 3y + 1 then we know the gradient is 2/3.

Hence we know the equation for a family of infinite parallel line is y = ²/₃ x + n (where n is any number).

We don't yet know b₂, the specific value of n that we need. But we know the point (20,-3) is on the line, so we can substitute these values:

(-3) = ²/₃ (20) + b₂

-3 - 40/3 = b₂

b₂ = -⁴⁹/₃

Hence the required equation is y = ²/₃ x - ⁴⁹/₃ OR 3y = 2x - 49 (to get rid of fractions)

Using the above method you should be able to derive the required function from your starting line, which wasn't included in the question.