SOLUTION: Find an equation for the line perpendicular to the line 5x - 15y = -2 having the same y-intercept as -9x -8y =24

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Question 1059735: Find an equation for the line perpendicular to the line 5x - 15y = -2 having the same y-intercept as -9x -8y =24
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
convert 5x - 15y = -2 to slope intercept form as follows:

subtract 5x from both sides of the equation to get:
-15y = -5x - 2
divide both sides of the equation by -15 to get:
y = -5/-15 * x - 2/-15.
simplify to get y = 1/3 * x + 2/15.

if your line is going to be perpendicular to this line, then the slope of your line must be be a negative reciprocal of 1/3.

the slope of your line must therefore be -3.

take the general form of the slope intercept form of a straight line and replace y = mx + b with -3 for m to get:

y = -3x + b.

all you now need to do is find b which is the y-intercept.

you are told it should the same y-intercept as -9x - 8y = 24.

to find that y-intercept, convert that equation to slope intercept form as follows:

start with -9x - 8y = 24
add 9x to both sides of the equation to get:
-8y = 9x + 24
divide both sides of that eqution by -8 to get:
y = -9/8 * x + 24/-8
simplify to get:
y = -9/8 * x - 3

your y-intercept has to be equal to -3.

replace b in y = -3x + b with -3 to get:
y = -3x - 3.

that should be your equation.

the following graphs show what is happening when the equations of both lines are kept in slope intercept form.

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you can also convert your perpendicular equation to standard form as follows:

start with y = -3x - 3
add 3x to both sides of the equation to get 3x + y = -3

the equation is in standard form.

your two equations in standard form are:

5x - 15y = -2 (original equation)
3x + y = -3

this particular graphing software can graph the lines in standard form.

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both graphs are the same, as they should be.

you can see that the blue line is perpendicular to the red line and that the blue line intersects the y-axis at y = -3.