Write an equation of the line containing the point (2,5) and perpendicular to the line 5x-2y=3

Answer 1

For the equation of a line given in Standard From, Ax+By=C , the slope is (-A/B). You may convert the equation to slope-intercept form and verify this.

Perpendicular lines have a slope that is the negative reciprocal. Thus, the line we seek has a slope of (B/A) and an equation that looks like: Bx-Ay=D [again, convert to/from slope-intercept form]

Given 5x-2y=3, the perpendicular line is 2x+5y=D and it contains the point (2,5)

2(2) + 5(5) = 29

2x + 5y = 29

With a little practice, this saves lots of time on standardized tests (where speed is important and calculations are not important).

Answer 2

The slope of the perpendicular is -2/5 (i.e. the negative reciprocal of the line to which it is perpendicular.

Then -2/5=(y-5)/(x-2), which can be manipulated into any needed form.