For the equation =7−12 which value represents the slope of a line perpendicular to the equation?

Perpendicular lines have opposite, reciprocal slopes.
For example, if one line had a slope of 4/5, then a perpendicular line would have a slope of -5/4.

The slope-intercept equation for a (non-vertical) line is:
y = mx + b
where m is a number representing the slope of the line and b is a number representing the y-intercept of the line.

We know already that m = -3/2 for our perpendicular line.
Also, our line will have the same x-intercept as the given line. We should probably find that point.
We can do that by setting y= 2/3x-6 equal to 0 and solving for x.
0 = 2/3x - 6
6 = 2/3x
6(3/2) = x = 9
The x-intercept is therefore at (x, y) = (9, 0).

Step 2. Determine "b" for our line. So far we have the equation:
y = -3/2x + b
We know this line goes through the point (x, y) = (9, 0). This means that when we plug in 9 for x in the equation of our line, we should get a value for y of 0.
0 = -3/2(9) + b
27/2 = b

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