Determine if the following equations form a perpendicular line or not

Slope-Intercept Form: y = mx + b, with m = slope and b = y-intercept.

If two lines are perpendicular, then they will have slopes that are negative reciprocals to each other. An example of negative reciprocals are 2 and -1/2

6.

Now with line 2, I have to convert it to slope intercept form. Firstly, subtract 2x on both sides of the equation:

Next, divide both sides by -5 and your slope-intercept form is

Now since 2/5 is not the negative reciprocal of -2/5, these lines are not perpendicular.

7.

It's pretty much the same process; convert to slope-intercept and determine if negative reciprocal. This time I'll brush through them:

Now since 2 is the negative reciprocal of -1/2, these lines are perpendicular.

Mathematical Induction is used in proving the statement is which holds the element in processing another statement and also proves that it is the key to proceed to another statement. In geometry, it is used to proved that the present geometric pattern hold the element in continuing in predicting the next geometrical pattern and also the next pattern also has this element.