Find the equation of the line that is parallel to 5x – 2y = -12 and passes through (-2, 3)

Answer 1

Skip to the summary for a quick answer:

The most efficient form to answer in is the Point-Slope form of a line which is in the form y - y₁ = m (x - x₁) where (x₁, y₁) is any point on the line.

We've already been given a the point (-2,3) so we can assume that x₁=-2 and y₁=3. All we need to solve for is the slope.

Parallel lines have the same slope so if we find the slope of the line we were given we will also have the slope our our line through (-2,3).

The equation 5x - 2y = -12 is in standard form Ax + By = C where A = 5, B = -2 and C = -12. The slope of a line in Standard form is m = -A / B therefore the slope is -5 / -2 or 5/2.

Therefore the equation of the line (in Point-Slope Form) is

y - 3 = (5/2) (x - ^-2) or y - 3 = (5/2) (x + 2).

You might be expected to write the equation in Slope-Intercept form or Standard form. If so please ask about how to convert from point slope form to one of the of the other forms.

Summary:

y - y₁ = m (x - x₁)

x₁=-2

y₁=3

m = -A / B= -5 / -2 or 5/2

Therefore substitute and get: y - 3 = (5/2) (x + 2)

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