To determine the slope of a line that is perpendicular to another line, we first need to find the slope of the given line. The equation provided is:
3y + 4x – 2 = 0
Let’s rearrange this equation into the slope-intercept form, which is y = mx + b, where m represents the slope.
We start by isolating y. Here are the steps:
- Subtract 4x from both sides:
3y = -4x + 2
- Divide every term by 3 to solve for y:
y = -\frac{4}{3}x + \frac{2}{3}
Now we can see that the slope (m) of the given line is -\frac{4}{3}.
For two lines to be perpendicular, the slopes will have a relationship defined as:
If m1 is the slope of the first line and m2 is the slope of the second line, then:
m1 × m2 = -1
In this case, we have:
m1 = -\frac{4}{3}
To find the slope (m2) of the line that is perpendicular, we can substitute:
-\frac{4}{3} × m2 = -1
Now, solving for m2:
1. Multiply both sides by -1:
\frac{4}{3} × m2 = 1
2. Now, multiply both sides by the reciprocal of \frac{4}{3}, which is \frac{3}{4}:
m2 = 1 × \frac{3}{4} = \frac{3}{4}
Thus, the slope of the line that is perpendicular to the line whose equation is 3y + 4x – 2 = 0 is \frac{3}{4}.