The slopes of the original function y = |x| are m = 1 and m = -1 (m is the variable used to represent slope).
when you add a coefficient (number) in front of |x|, it will either make the slopes steeper or more flat. the larger the value of the coefficient, the steeper the slope will be (vice versa for a coefficient smaller than 1, which would make the slope more flat than the parent(original) function).
because these are absolute value functions, they will have two slopes. one slope for the end going up from left to right, and one for the end going down from left to right. this means that one slope must be positive and the other slope must be negative for each function.
with this in mind, the slopes of y = 2|x| are m = 2 and m = -2. the coefficient of 2 narrows the function by a factor of 2 (it is twice as narrow as the parent function). the same rules apply to y = 4|x| with the slopes of this function as m = -4 and m = 4 (it is 4 times narrower than the parent function).
with the fraction coefficients, the function is being widened. therefore, the slopes of y = 1/2 |x| are m = -1/2 and m = 1/2. the slopes of y = 1/5 |x| are m = -1/5 and m = 1/5.
Answer:
Incorrect
Step-by-step explanation:
The correct answer is A.
The slope-intercept form is y-y₁=m(x-x₁)
The problem with B is that if you take out the coordinates for x₁ and y₁, you get the coordinates (1,4). This coordinate does not land on the line.
The coordinates for A is (-1,4). This point does land on the line.
Answer:
1/5
1. 1/56
2. 1/6
3. 1/65
4. 1/7
5. 1/75
1/8
Step-by-step explanation:
The fractions I gave (1/56, 1/6, 1/65, 1/7, 1/75) are all in between 1/5 and 1/8.
A way to think about this is to add a zero to a denominator of 1/5 and 1/8 and turn them into whole numbers:
1/5 --> 1/50 --> 50
1/8 --> 1/80 --> 80
Then find number between them:
55, 60, 65, 70, 75
Then, turn them into a fraction with a 1 as the numerator and the number as denominators:
1/55, 1/60, 1/65, 1/70, 1/75
This is the process. These numbers are all in between 1/5 and 1/8.
I hope this helps you!
(P.S., I don't think this works with negative numbers, though)
