How can you determine if two lines are perpendicular? How can you tell if two lines are parallel? State whether the following sets of lines are parallel, perpendicular or intersecting. Then explain why.
1) y = x + 4
y = x - 3
2) y = 3x - 7
y = -1/3 x + 10
3) y = 3x -7
y = -3x + 10
Two lines are parallel if they have the same slope
Two lines are perpendicular if their slopes are the opposite reciprocals of each other.
since all your equations are in the form
y = mx + b, and m is the slope,
you can find your result by just looking at them.
Reiny, you stated, i can find my result by just looking at them, but I'm not exaclty sure about that.
1) y = x + 4
y = x - 3
2) y = 3x - 7
y = -1/3 x + 10
3) y = 3x -7
y = -3x + 10
I've gotten different answers on whether the sets of lines are
parallel, perpendicular or intersecting. My first answer is that all the sets are parallel, but then I second guessed myself and said all the 1st line of each set is parallel and the 2nd lines are perpendicular. Can you confirm if my 1st answer is correct, if not, why?
Remember that:
"y = mx + b, and m is the slope, "
For the first one:
1) y = x + 4
y = x - 3
"Two lines are parallel if they have the same slope "
Knowing that "x" is a short form for "1x" where slope=m=1, can you deduce whether they have the same slope?
You can take it from here for the rest.
To determine if two lines are perpendicular, we need to check their slopes. If the slopes of the lines are negative reciprocals of each other (meaning that multiplying the slopes together gives -1), then the lines are perpendicular.
To determine if two lines are parallel, we need to check their slopes. If the slopes of the lines are the same, then the lines are parallel.
Now let's apply these concepts to the given sets of lines:
1) y = x + 4 and y = x - 3
To find the slopes of these lines, we can observe that both have a coefficient of 1 in front of the x term. Therefore, the slopes of both lines are equal to 1. Since the slopes are the same, these lines are parallel.
2) y = 3x - 7 and y = -1/3 x + 10
The first line has a slope of 3, while the second line has a slope of -1/3. Since these slopes are not equal, the lines are not parallel. To check if they are perpendicular, we can multiply the slopes together: 3 * (-1/3) = -1. Since the product of the slopes is -1, these lines are perpendicular.
3) y = 3x - 7 and y = -3x + 10
The first line has a slope of 3, while the second line has a slope of -3. Since these slopes are not equal, the lines are not parallel. To check if they are perpendicular, we can multiply the slopes together: 3 * (-3) = -9. Since the product of the slopes is not -1, these lines are not perpendicular either.
In summary:
1) The lines y = x + 4 and y = x - 3 are parallel because their slopes are equal.
2) The lines y = 3x - 7 and y = -1/3 x + 10 are perpendicular because their slopes are negative reciprocals of each other.
3) The lines y = 3x - 7 and y = -3x + 10 are neither parallel nor perpendicular because their slopes are different, but the product of their slopes is not -1.