HELP PLS!, How do i find the value of a if 2x + 5y = 11 and ax - 3y = 9 are perpendicular?

Question

Please help me out guys, and if u can show all working out and the answer

Answer 1

(x=3) (2X3=6) (y=1) (5X1=5) = (6+5=11)

Answer 2

first find out the slopes of both lines [u can use the formula as

slope(m)= -coefficient of x/ coefficient of y].....let each of them m1 and m2......then since the lines are perpendicular use, (m1*m2+1=0)

then u can put those slopes in this equation and find the value of a.

here,

    m1= -2/5  and  m2= a/3  

then,

     m1*m2+1=0

or, -2a/15= -1

or, 2a=15

or, a= 15/2.......:-}

Answer 3

put each rule into the form y=mx+c to find the slope of each line.

5y=-2x+11 has a gradient (slope) of -2/5  Call this m1 (m subscript1)

Now the second line is changed to 3y=_ax-9.

Divide this through by 3 to give the coefficient of x as a/3.

y=a/3times x -9

the slope of this line is a/3.  Call this m2.

Now to be perpendicular the two slopes must multiply together to give -1.  That is m1 by m2 =-1. This means (-2/5)by (a/3) =-1

i think this gives a=15/2

(Note that m in y=mx+c is the slope)

Answer 4

Perpendicular lines have opposite repciprocal slopes (slopes that equal -1 when multiplied together). Solve both for y.

2x+5y=11

5y= -2x+11

y= (-2/5) x + (11/5)

So, you have to multiply -2/5 by something that will make it -1 : 5/2.

ax-3y=9

-3y= -ax +9

y= (a/3)x - 3

That means (a/3)= (5/2)

(a/3)= 5/2

3* (a/3)= 3* (5/2)

3's cancel out

a=15/2

Answer 5

Everything the first answerer did is correct, except for the conclusion.  Saying either gradient is the negative reciprocal of the other is the same as saying their product is -1, so you can write

(-2/5)*(a/3) = -1

therefore

-2a/15 = - 1

2a = 15

a = 15/2 = 7.5

OR ELSE you could start by saying a line perpendicular to the first one has gradient +5/2  (change sign, and invert)

Therefore a/3 = 5/2

a = 3*5/2

a = 7.5

PS notice Judy M is correct except for that little slip in the last step.  There's a minus on both sides, so the answer is positive.

Answer 6

you would know if they have the opposite reciprocal slops.

so 2x + 5y = 11 would turn into y = -(2/5)x + 11/5

divide by 5 on all sides to isolate the y and move the x over

and ax -3y = 9 would turn into  y = (a/3)x + 9

move the ax over and divide by -3 on all sides

since they are not opposite reciprocals it is clear that these linesare not perpendicular.

i hope this helps, i couldnt show every step on the comp, its easier to do by hand but i think you can basically figure it out