Question

The equation of line m is 3x−5y=−4.

Answer 1

The slope is -5/3 but the equation is y=-5/3x+b. Find this by flipping and switching the other slope to opposite. OG slope: 3/5 so perpendicular line would have a negative slope and the 3 and 5 are switched. Make sense?

Answer 2

First, write your equation in slope-intercept form, or form y = mx + b:
1) Solve for 5y:
3x - 5y = -4
3x + 4 = 5y
2) Divide everything by 5:
y = 3x/5 + 4/5
Now, we got it.
In this line slope is 3/5 because it is multiplier for x, and, the rule is that
m * p = -1
where m is the slope of the line, and p is the slope of the line perpendicular to this.
3) Now, solve there for p by plugging in value for m:
p = -1/m
p = -1 / (3/5) = -5/3
4) Now just write the equation in this form: y = px + b:
y = -5x/3 + b
This is the equation of the line perpendicular to the given one. Hope this helps!