Which equation represents the line that is perpendicular tot the line 5x-2y=-6 and passes through the point (5,-4)

Answer 1

1. When given the point and a equation and you are trying to find the equation that passes through a given point, you need to use the point slope formula, provided below.

y - y₁ = m (x - x₁)

1. Now lets see what is given. We are given the point (5, -4) where 5 is your x₁ and -4 is your y₁.
2. The equation of the line given is 5x - 2y = 6. We need to convert this equation to y = mx + b form so we can find the slope.

5x - 2y = 6

-2y = -5x + 6

2y = 5x - 6

y = 5/2x -3

1. Now that we have put the equation in the proper form we know that the slope is 5/2x.
2. Looking back at the question, it states that we are trying to find the equation that is perpendicular to the equation we just re-wrote. Perpendicular slope means negative reciprocal.
3. So we take our slope of 5/2x, we flip it and add a negative, and we get -2/5x
4. Our slope is (m) and we have the point, so we have everything we need and now we just plug it into the point-slope formula.

y - y₁ = m (x - x₁)

y - (-4) = -2/5 (x - 5)

y + 4 = -2/5x + 2

1. Your final awnser y = -2/5x -2

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