Question

Explain how to write an equation for the line that contains the point (2, -3) and is perpendicular to the

graph of x + 2y = 2

Answer 1

`y=2x-7`

Explanation:

Convert to slope-intercept form

`x+2y=2\\\\2y=2-x\\\\y=1-(1)/(2)x\\ \\y=-(1)/(2)x+1`

Find the opposite reciprocal slope

Original -->
`-(1)/(2)`

Opposite Sign -->
`(1)/(2)`

Reciprocal -->
`2`

Find the new y-intercept given the point (2,-3)

`y=2x+b\\\\-3=2(2)+b\\\\-3=4+b\\\\b=-7`

Final Equation

`y=2x-7`