1. Determine whether the lines given by the equations 2x + 3y = and y=3/2x+4
are perpendicular.

2. Two lines having the same -intercept are perpendicular. If the equation of one of
these lines is y= −4/5x+6, what is the equation of the second line?

1. Yes, the lines are perpendicular.

2.

Step-by-step explanation:

The first equation of Exercise 1 is incomplete. Let's assume that it is:

Where "n" is a number.

First, it is important to remember that the equation of a line in Slope-Intercept form is:

Where "m" is the slope and "b" is the y-intercept.

By definition, the slopes of perpendicular lines are negative reciprocals.

1 . If you solve for "y" from the first equation, you get:

You can identify that the slope is:

The second equation of the line is:

And its slope is:

Since the slopes are negative reciprocals, the lines are perpendicular.

2. Given the first equation of the line:

You can identify that:

Since the first line and the second one are perpendicular, you know that the slope of the other line is:

According to the information given in the exercise, both lines have the same y-intercept; therefore, the equation of the second line is:

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step-by-step explanation:

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