Question

Find the equation of the line which passes through the point (2,5)

, and is perpendicular to the line with the equation y=−23x+4
. Express your answer in slope-intercept form. Simplify your answer.

Answer 1

`y=(1)/(23)x+(113)/(23)`

Explanation:

Perpendicular slopes will have opposite reciprocal slopes, so the slope of the perpendicular line will be 1/23, and we can determine the y-intercept of that function:

`y=(1)/(23)x+b\\\\5=(1)/(23)(2)+b\\\\5=(2)/(23)+b\\\\115=2+23b\\\\113=23b\\\\b=(113)/(23)`

Therefore, the equation of the line which passes through the point (2,5), and is perpendicular to the line with the equation y = −23x+4 is
`y=(1)/(23)x+(113)/(23)`