Find the slope of a line perpendicular to the line defined by the equation 3x-5y=12

-5/3

Step-by-step explanation:

Note the slope intercept form: y = mx + b

Note that:

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

Isolate the variable, y. First, Subtract 3x from both sides:

3x (-3x) - 5y = 12 (-3x)

-5y = -3x + 12

Next, divide -5 from both sides. Remember to divide from all terms within the equation:

(-5y)/-5 = (-3x + 12)/-5

y = (-3x/-5) + (-12/5)

Simplify.

y = (3x/5) - 12/5

y = (3/5)x - 12/5

You are trying to find the perpendicular slope to this line. To do so, simply flip the slope (m) as well as the sign:

Original m = 3/5

Flipped m = -5/3

-5/3 is your perpendicular slope.

          5                                

m =  -    perpendicular slope

          3

Step-by-step explanation:

3x - 5y = 12 >> convert to y = mx + b

- 5y = - 3x + 12

- 5y = - (3x + 12) --- eliminate the negative

5y = 3x + 12

     3x + 12

y =

         5

       3           12

y = x  +  

       5            5  

the above equation is the form of  y = mx + b

where m is the slope and b is the intercept

                            5                                

therefore,  m =  -    perpendicular slope

                             3                        

astronomers is your final answer! : )

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions