Since y=2x+1 does not pass through the origin (i.e. there exists the constant term of 1 ), the variables y and x are not directly proportional - though, they do have a linear relationship.
Answer:
the answer is d
Step-by-step explanation:
so for one do y-intercept has to be at (0,25) so we can eliminate answer choices B and C
the reason why it is not a is because a is moving out of constant rate of 25 when it needs to be moving at a constant rate like 10 D is the answer because it's moving at a constant rate of 10 and it has a y intercept of (0,25)
Answer:
y = 3x - 16
Step-by-step explanation:
We are asked to find the equation of the line perpendicular to 2x + 6y = 30
We can use two formulas for this question, either
y = mx + c. Or
y - y_1 = m(x - x_1)
Step 1: calculate the slope
From the equation given
2x + 6y = 30
Make y the subject of the formula
6y = 30 - 2x
Or
6y = -2x + 30
Divide both sides by 6, to get y
6y/6 = ( -2x + 30)/6
y = (-2x + 30)/6
Separate them in order to get the slope
y = -2x/6 + 30/6
y = -1x/3 + 5
y = -x/3 + 5
Slope = -1/3
Step 2:
Note: if two lines are perpendicular to the other, both are negative reciprocal of each other
Perpendicular slope = 3/1
Substitute the slope into the equation
y = mx + c
y = 3x + c
Step 3: substitute the point into the equation
( 6,2)
x = 6
y = 2
2 = 3(6) + c
2 = 18 + c
Make the c the subject
2 - 18 =c
c = 2 - 18
c = -16
Step 4: sub the value of c into the equation
y = 3x + c
y = 3x - 16
The equation of the line is
y = 3x - 16
If you try out the other formula, u will get the same answer
Let's assume that the statement "if n^2 is odd, then is odd" is false. That would mean "n^2 is odd" leads to "n is even"
Suppose n is even. That means n = 2k where k is any integer.
Square both sides
n = 2k
n^2 = (2k)^2
n^2 = 4k^2
n^2 = 2*(2k^2)
The expression 2(2k^2) is in the form 2m where m is an integer (m = 2k^2) which shows us that n^2 is also even.
So this contradicts the initial statement which forces n to be odd.