L1 is parallel L2 and L3 is perpendicular to L2. If m3=-2/3, find m1

How am I supposed to answer this and what formula should I use? I'm really studying hard right now yet my teacher is quiet off and I cant find the right words to search it on internet.

perpendicular lines with slopes m1 and m3 obey

m1 * m3 = -1

did you try googling slopes of perpendicular lines?
If not, you didn't try very hard.

I sould try harder, by the way thank you very much!

To find the value of m1, we can use the fact that parallel lines have the same slope, and perpendicular lines have slopes that are negative reciprocals of each other.

Given that L1 is parallel to L2, we can say that m1 = m2.

We are also given that L3 is perpendicular to L2, which means that m3 (the slope of L3) is the negative reciprocal of m2.

We are given that m3 = -2/3, therefore m2 = -1/m3 = -1/(-2/3) = 3/2.

Since m1 = m2, we can conclude that m1 = 3/2.

To find m1, the slope of line L1, we can utilize the fact that L1 is parallel to L2. When two lines are parallel, they have the same slope.

Given that L2 is parallel to L1, we need to find the slope of L2 first. However, the information provided does not include the slope of L2 directly.

Fortunately, we are also given that L3 is perpendicular to L2. When two lines are perpendicular, their slopes are negative reciprocals of each other.

Therefore, we can determine the slope of L2 by taking the negative reciprocal of m3.

Given m3 = -2/3, the negative reciprocal of -2/3 is 3/2. Therefore, the slope of L2 is 3/2.

Since L2 is parallel to L1, m1 = 3/2.

Hence, m1 = 3/2.

To recap:
1. Determine the negative reciprocal of m3, which is the slope of L2.
2. Since L1 is parallel to L2, m1 will be the same as the slope of L2.
3. Hence, m1 = 3/2.