find the slope of the line that is perpendicular to the line whose equation is 5x-7y=12

The slope of the given equation is 5/7

the slopes of perpendicular lines have slopes that are opposite reciprocals of each other.
so the perpendicular line has slope -7/5

To find the slope of a line that is perpendicular to another line, you need to determine the slope of the given line first.

Step 1: Convert the equation of the line into slope-intercept form (y = mx + b), where m represents the slope of the line.
Given equation: 5x - 7y = 12
Rearrange the equation to isolate y:
-7y = -5x + 12
Divide both sides by -7:
y = (5/7)x - 12/7

Now you can see that the slope of the given line is 5/7.

Step 2: Determine the slope of the line perpendicular to the given line.
Remember that the slopes of perpendicular lines are negative reciprocals of each other. This means if the slope of one line is m, then the slope of the perpendicular line is -1/m.

In this case, the slope of the given line is 5/7.
So, the slope of the line perpendicular to the given line is -1/(5/7), which is equal to -7/5.

Therefore, the slope of the line that is perpendicular to the line with the equation 5x - 7y = 12 is -7/5.