Write an equation that is perpendicular to 3x-5y=5 and passes through the point 9 and -14

Answer 1

Hello Kaylnn,

Thank you for your question.

A few items to put into your memory bank that you will use over and over again.

The slope intercept form of an equation is

y = mx + b

Where m is the slope and b is the y intercept

If you want an equation, that is perpendicular to an equation you find the negative inverse of the original equation’s slope

The general form of an equation is

ax + by = c

let’s take the original equation and put it into slope, intercept form, and then take the slope and find the negative inverse

3x - 5y = 5

now subtract 3X from both sides

-5y = -3x + 5

Divide through by -5

y = (3/5)x - 1

slope is 3/5

To get slope that is perpendicular take the negative inverse. -5/3

General slope intercept form of new equation to start with

y = (-5/3)x + b

substitute x=9 and y= -14 into equation above and solve for b

-14= (-5/3)9 + b

-14 = -45/3 + b

-42/3 + 45/3 =1 = b

substituting in to slope intercept form

y = -5/3x + 1

Rearranging into general form

5/3x + y = 1

Answer 2

Hi Kaylnn,

Perpendicular lines have negative reciprocal slopes, and the slope of any line is the "m" in the equation:

y = mx + b

Your equation is in general form, so our first task is converting to slope-intercept:

3x - 5y = 5

Subtract 3x from both sides

-5y = -3x + 5

Divide both sides by -5

y = 3/5x -1

Slope of your line is 3/5; negative reciprocal is -5/3. Now, we need the full equation of the line, though, so we plug the point in for x and y in y = mx + b. We also use the perpendicular slope for m and solve for b:

-14 = -5/3 (9) + b

-14 = -15 + b

b = 1

Equation in slope-intercept form is:

y = -5/3x +1

If your instructor wants general form Ax + By = C, then:

-5/3x - y = -1

Clear the fraction by multiplying by -3:

5x + 3y = 3

I hope this helps.