What is the slope of a line perpendicular to 2x + 4y = 5?
How would I figure this out? Thank you so much! :)
You are probably used to reading the slope from an equation in the form y = mx + b so let's change it to that
2x + 4y = 5
4y = -2x + 5
y = (-2/4)x + 5/4
so the slope of the given line is -1/2
recall that slopes of perpendicular lines are "opposite reciprocals" of each other
so the new line has slope +2
This is a different problem...
Find the distance between A (0,1) and B (4,5).
Is this like the slope?
the calculations might look similar, but the concept is much different.
you should have seen the formula
distance = √[(change in x's)^2 + (change in y's)^2]
= √[(4-0)^2 + (5-1)^2]
= √[16+16]
= √32
notice the same calculation as deltax and deltay ?
Well, to find the slope of a line perpendicular to another line, you need to first find the slope of the original line. In this case, we have the equation 2x + 4y = 5. Let's first rearrange it to get it in the form y = mx + b, where m represents the slope:
4y = -2x + 5
y = -(2/4)x + 5/4
y = -(1/2)x + 5/4
So the slope of the original line is -1/2.
Now, to find the slope of a line perpendicular to this one, you need to take the negative reciprocal of the slope. So the slope of the line perpendicular to 2x + 4y = 5 is 2.
Therefore, the slope of a line perpendicular to 2x + 4y = 5 is 2.
To find the slope of a line perpendicular to another line, you need to determine the slope of the given line first.
Step 1: Convert the given equation to the slope-intercept form (y = mx + b), where "m" represents the slope.
Start by isolating the "y" term on one side:
2x + 4y = 5
4y = -2x + 5
Divide both sides by 4:
y = (-2/4)x + 5/4
Step 2: Identify the slope of the given line:
The equation is now in slope-intercept form (y = mx + b), where m = -2/4.
Therefore, the slope of the given line is -2/4, or simplified as -1/2.
Step 3: Determine the slope of the line perpendicular to the given line:
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.
In this case, the negative reciprocal of -1/2 is 2/1, or simply 2.
Hence, the slope of a line perpendicular to 2x + 4y = 5 is 2.