SOLUTION: the lines with equations x + 2y = 3 and 3y + Ax = 2 are perpendicular to each other . find the value of A a -6 b -3/2 c 3/2 d 6 e 22

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Question 252431: the lines with equations x + 2y = 3 and 3y + Ax = 2 are perpendicular to each other . find the value of A
a -6 b -3/2 c 3/2 d 6 e 22
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the 2 equations are in standard form of ax + by = c

the slope intercept form of these equations would be y = mx + b where m is the slope and b is the y-intercept (value of y when x = 0).

the easiest thing for you to do is to transform the standard form of these equations into the slope-intercept form of them.

all you do is solve for y and this happens automatically.

your first equation is:

x + 2y = 3

subtract x from both sides of this equation to get:

2y = -x + 3

divide both sides of this equation by 2 to get:

y = -(1/2)*x + (3/2)

your slope is -(1/2).
your y-intercept is (3/2).

your second equation is:

3y + Ax = 2

subtract Ax from both sides of this equation to get:

3y = -Ax + 2

divide both sides of this equation by 3 to get:

y = -(A/3)*x + (2/3)

your slope is -(A/3).
your y-intercept is (2/3).

in order for the lines formed by these equations to be perpendicular, the slopes have to be negative reciprocals of each other.

the two slopes you have to work with are:

-(1/2) and -(A/3).

the negative reciprocal of a number is equal to -1 divided by the number.

the negative reciprocal of -(1/2) = -1/-(1/2).

this comes out to be equal to 2.

in order for the lines of these equations to be perpendicular to each other, -(A/3) must be equal to 2 which is the negative reciprocal of -(1/2).

your equation to solve is:

-(A/3) = 2

multiply both sides of this equation by 3 to get:

-A = 6

multiply both sides of this equation by (-1) to get:

A = -6

your answer is A = -6.

your original equations were:

x + 2y = 3 and 3y + Ax = 2

replace A with -6 to get:

x + 2y = 3 and 3y - 6x = 2

to graph these equations, we need to solve for y which automatically puts them into the slope-intercept form.

we get:

y = -(1/2)*x + (3/2) and y = (6/3)*x + (2/3)

the second equation simplifies to:

y = 2*x + (2/3) because 6/3 is the same as 2.

the graph of these equations looks like this:

y = -(1/2)*x + (3/2) crosses the y-axis at (3/2) = 1.5. This graph slopes down from left to right.

y = 2*x + (2/3) crosses the y-axis at (2/3) = .66666667. This graph slopes up from left to right.