Search 74,123 tutors
0 0

Put the following two equations in slope-intercept form and show that they are Perpendicular.

Put the following two equations in slope-intercept form and show that they are Perpendicular.2x – 3y = 5 and 3x + 2y = 7.

The slope intercept form for equations will be

y = (2/3)x - 5/3 -----------------(1)

y = (-3/2)x + 7/2 ----------------(2)

As, you can see that slopes in both the equation are reciprocal and negative. That's why the lines are perpendicular to each other.

Hope this helps you. Do the work to make the equations in slope-intercept form. If you still have difficulty, we're there to help you out.

Hi, Henriettas --

Slope-intercept equations have the form y = mx + b, where is the slope and is the y-intercept.

We will do these one at a time:

2x - 3y = 5         we need to piut the 2x term on the right:
-2x            -2x
________________

-3y  =  -2x + 5         now divide both sides by -3 to leave a positive y =
y  =  (2/3)x - 5/3

The slope is 2/3.

For the second one, we will follow the same steps:

3x + 2y  =  7      move 3x to the right:
-3x             -3x
________________

2y  =  -3x + 7      divide by 2:
y  =  (-3/2)x + 7/2

The slope is -3/2.

Perpendicular lines have slopes that are negative reciprocals of each other.

-3/2 is the negative reciprocal of 2/3, so these two lines are perpendicular.

1) 2x-3y=5      => y= 2x/3 -5/3

slope = 2/3

2) 3x+2y=7    => y=-3x/2 +7/2

slope = -3/2

if we multiply both slopes (-3/2) * (2/3) the naswer is -1 and that means they ar Perpendicular!