The equation is currently in standard form, which makes it a little challenging to find the slope. However, we can rearrange the equation into slope-intercept form to get the slope.
1.) Rearrange the equation from Ax+By=C form to y=mx+b form:
5x-3y=2
Subtract 5x from both sides:
-3y=-5x+2
Isolate y by divided by -3 on both sides:
y=(-5/-3)x-2/3
A negative number divided by a negative number is a positive quotient:
y=5/3x-2/3
Now that we have the slope of the equation, we can find the slope of a line perpendicular to it:
Perpendicular slope of any line: m——> -1/m, where m is the slope.
Essentially, we take the negative reciprocal of the initial line’s slope.
So, the slope is 5/3 and we will take it’s negative reciprocal:
5/3——>-3/5
Therefore, your answer is -3/5