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