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Question

PLEASE NO OPINIONS ONLY ANSWERS!!!!!!
try to help me or something don't be mean.
1.Explain why the x and y intercepts of a direct variation are always zero.
2.Write the equation of a line parallel to y=0.5x - 10.
PLEASE SHOW ME STEPS TO SOLVING THIS;
write an equation of a line that satisfies given conditions.
a. parallel to y= 5x, through (2,-1) * how do u solve that, explain to me *

Answer 1

1. A direct variation relationship actually is described by the equation of a straight line, so if y varies directly as x then y = kx, where k is a constant of proportionality. When you are talking about straight lines, k is actually the same thing as the slope of the line. Take a look at what happens when we let x and y assume the value of 0 in a direct variation equation:

y = kx:

x = 0 -----> y = k(0) = 0
So when x = 0, y also is 0.

y = 0 -----> 0 = kx -----> 0 / k = x = 0
So when y = 0, x is 0.

That's why the x and y intercercepts of a direct variation are always zero. Whenever one variable is zero, the other is forced to be zero also. By the way, the intercepts just also happen to coincide with the origin of the Cartesian coordinate plane, (0,0).

2. For a line to be parallel to another line, they must both have the same slope. The only thing that will be different is the y-intercept of their equations. In the equation y = 0.5x - 10, the slope of the line is 0.5, which is the same thing as 1/2. The y-intercept is -10. You can write an equation for a line which is parallel to this by simply giving it a different y-intercept. If we write y = 1/2x + 10, then we have an equation with the same slope, but which intersects the y-axis at +10 instead of -10.

In your particular problem, y = 5x, the slope is 5, and the y-intercept is 0, because there is no second term. What they want you to do is find an equation in the form y = 5x + k, where 5 is the slope of the line, and k is its y-intercept, so what when you plug 2 into this equation, the result, y, is equal to -1. So all you have to do is plug the two numbers, x = 2 and y = -1, directly into y = 5x + k and find out what k must equal in order to make the equation true.

y = 5x + k
-1 = 5(2) + k
-1 - 10 = k
-11 = k

Now plug your calculated value for k back into your original equation, y = 5x + k, to see if a true statement results. If it does, then you have the right number.

-1 = 5(2) - 11
-1 = 10 - 11
-1 = -1

It does! So the solution is correct.

The equation you want then is y = 5x - 11

Answer 2

1.Explain why the x and y intercepts of a direct variation are always zero.
Sorry about this one, but I have no clue.

2.Write the equation of a line parallel to y=0.5x - 10.
Since it's parallel, the number in front of the x is the same. Just change the number on the end, like this: y=0.5x+6

a. parallel to y= 5x, through (2,-1)
If you plug in the x- and y- values, you get: -1=10 which doesn't work. Therefore you must subtract 11 from 5x to make the equation even so it will look something like this: y=5x-11