Given line = 5x – 2y = 10
Find the slope for a line parallel to the given line
Find the slope for a line perpendicular to the given line
change to the form y = mx + b, the value of m will be the slope
5x - y = 10
-y = -5x + 10
y = 5x - 10
the slope is 5
perpendicular lines have slopes that are the opposite reciprocals of each other.
so if the first slope is 5, the slope of the perpendicular is -1/5
So is the slope of the given line 2.5? I don't need to know that, but just wanted to make sure. Thanks!
yes, or 5/2
making the slope of the reciprocal - 2/5
But that is for the given line not the parallel or perpendicular one? So what I see is as follows and is correct?
a. For the Parallel slope we change to the form y = mx + b, and the value of m is the slope
5x - 2y = 10
-y = -5x + 10
y = 5x - 10
the slope is 5
m = 5
Why are we using -y? isn't it -2y? or is this ok? How do we conclude it's 5?
AND for this one
b. Find the slope for a line perpendicular to the given line.
Perpendicular lines have slopes that are the opposite reciprocals of each other.
So if the parallel line slope is 5, the slope of the perpendicular line is -1/5 because it is the reciprical?
I just wanna be sure I am understanding this correctly! Thanks for you time and help!
You are right, I copied the equation incorrectly
I apologize for the confusion
here is the correct version:
5x - 2y = 10
-2y = -5x + 10
y = (5/2)x - 5
the slope is 5/2
perpendicular lines have slopes that are the opposite reciprocals of each other.
so if the first slope is 5/2, the slope of the perpendicular is -2/5
to get the slope of the perpendicular to any given line
... flip the slope and change the sign
e.g. first slope : -5/9
slope of perp. is +9/5
e.g. first slope = +6
slope of perp. is -1/6
Is this the slope to the parallel line and perpendicular line or for the given line of 5x – 2y = 10? I am a bit confused about this because I get 5/2 or 2 and 1/2 for the slope of the given line. Can you please explain further? Thanks!
I think I got it! Are the slopes of the given and parallel lines = ?
Beth good job! I think this is correct. Lets see what the experts have to say about this!
To find the slope of a line parallel to the given line, you need to know that parallel lines have the same slope. The given line is in the form of a standard linear equation: 5x - 2y = 10. To find the slope, rearrange the equation into slope-intercept form, which is y = mx + b, where m represents the slope:
5x - 2y = 10
-2y = -5x + 10
Divide both sides by -2:
y = (5/2)x - 5
Now, observe that the coefficient of x is equal to the slope, so the slope of the given line is 5/2. Therefore, any line parallel to the given line will also have a slope of 5/2.
To find the slope of a line perpendicular to the given line, you need to know that perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of 5/2 is -2/5. Therefore, any line perpendicular to the given line will have a slope of -2/5.