Determine which two equations represent perpendicular lines.
a)y=5/3
b)y=5x-5/3
c)y=-1/5x+5/3
d)y=1/5x-5/3
I have worked on this equation for two days.
B & C
If you negate and invert the slope of B, you get the slope of C
B slope: 5
C slope: -1/5
"I have worked on this equation for two days."
Well, you could have spend the two days better by learning some more maths :)
The answer is b) and c). Two lines:
y1 = m1 x + c1 and
y2 = m2 x + c2
are perpendicular if m1*m2 = -1
The reason why you have difficulties is because the problems you are given are too easy and can be solved by applying simple equations. If you only focus on these kind of problems you won't learn a lot and you'll continue to have difficulties.
The best way to learn maths is by trying to understand the fundamentals. Try to read this article:
http://en.wikipedia.org/wiki/Dot_product
To determine which two equations represent perpendicular lines, you need to compare their slopes. In general, two lines are perpendicular if the product of their slopes is -1.
Let's find the slopes of the given equations:
a) The equation y = 5/3 is in the form y = mx + b, where m represents the slope. The slope of this line is 5/3.
b) The equation y = 5x - 5/3 is also in the form y = mx + b. The slope of this line is 5.
c) The equation y = -1/5x + 5/3 is also in the form y = mx + b. The slope of this line is -1/5.
d) The equation y = 1/5x - 5/3 is also in the form y = mx + b. The slope of this line is 1/5.
Now, let's check which pairs of equations have slopes that multiply to -1:
- Option a (slope = 5/3) and option b (slope = 5):
(5/3) * 5 = 25/3
Since 25/3 is not equal to -1, options a and b do not represent perpendicular lines.
- Option a (slope = 5/3) and option c (slope = -1/5):
(5/3) * (-1/5) = -1/3
Since -1/3 is equal to -1, options a and c represent perpendicular lines.
- Option a (slope = 5/3) and option d (slope = 1/5):
(5/3) * (1/5) = 1/3
Since 1/3 is not equal to -1, options a and d do not represent perpendicular lines.
- Option b (slope = 5) and option c (slope = -1/5):
5 * (-1/5) = -1
Since -1 is equal to -1, options b and c represent perpendicular lines.
- Option b (slope = 5) and option d (slope = 1/5):
5 * (1/5) = 1
Since 1 is not equal to -1, options b and d do not represent perpendicular lines.
- Option c (slope = -1/5) and option d (slope = 1/5):
(-1/5) * (1/5) = -1/25
Since -1/25 is not equal to -1, options c and d do not represent perpendicular lines.
From our analysis, the pairs of equations that represent perpendicular lines are options a (y = 5/3) and c (y = -1/5x + 5/3), and options b (y = 5x - 5/3) and c (y = -1/5x + 5/3).