Question

What is the equation of the line that passes through the point (1, 3) and is perpendicular to the line 2x+3y=15?

Answer 1

y=2x+1

Explanation:

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Rearrange 2x+3y=15 by subtracting 2x by both sides. Dividing 3y by both sides.

1⇒
`2x-2x+3y=15-2x`

2⇒
`(3y=15-2x)/(3y)`

`y=5-(2)/(3) x`

We know this slope is negative. Meaning for the perpendicular crossing to work, it must have a positive slope. We know that 3=(1*M)+B. Perpendicular lines will have slopes that are negative reciprocals of one another.

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We know the slope must be between 1 and 3. We know the base must be between 1 and 3.

Using the slope formula y-y/x-x

`(5-3)/(0-1) \\ m=2`