Question

Input the equation for the following line in standard form Ax + By = C. Reduce all fractional answers to lowest terms.

A line with y-intercept of 2 that is parallel to 2x + y = -5.

Answer 1

Well, you know that for a line to be parallel it has to have the same slope. If you solve the equation for y you see that:
y=-2x-5
So the slope is -2.
Using slope-intercept form (y=mx+b)
you can write your new line as:
y=-2x+2 (the -2 we got from the fact its parallel, and the 2 is the y-intercept)
Then just rearrange it to standard form.
y+2x=2

Answer 2

could you help me with one more?

Answer 3

Sure :P

Answer 4

Given two points on the line, input the equation of the line in standard form Ax + By = C. Reduce all fractional answers to lowest terms.

(-8, 0), (1, 5)

Answer 5

Okay, firstly, you know that the slope of a line is:
\[m=\frac{\Delta y}{\Delta x}\]
So your change in y would be: 5-0=5
Your change in x would be 1-(-8)=9
So your slope is:
\[\frac{\Delta y}{\Delta x}=\frac{5}{9}\]
Then you need to use point slope form:
\[y-y_0=m(x-x_0)\]
Either point will work.
\[y-5=\frac{5}{9}(x-1) \rightarrow y-5=\frac{5x}{9}-\frac{5}{9}\]
Adding 5 to the right gives you:
\[y=\frac{5x}{9}+\frac{40}{9}\]
Then you want to put the x on the left side giving:
\[\frac{-5x}{9}+y=\frac{40}{9}\]
And if you wanted to be really clever you could multiply both sides by 9 to get ride of the denominator giving:
\[-5x+9y=40\]
Just to make it look nice. :P

Answer 6

could you help me with one more ? :)

Answer 7

Yeah go for it. I'm jumping around a few questions so it might take me a moment.

Answer 8

Given two points on the line, input the equation of the line in standard form Ax + By = C. Reduce all fractional answers to lowest terms.

(7, -3), (4, -8)

Answer 9

dont forget about me!

Answer 10

For this one you want to do the same thing. You want to find the change in y and x.
The change in y is -8-(-3)=-5
And the change in x is 4-7=-3
So your slope is 5/3.
Using point slope again you have:
y-(-3)=(5/3)(x-7)
\[y+3=\frac{5x}{3}-\frac{35}{3}\]
Subtracting 3 gives you:
\[y=\frac{5x}{3}-\frac{44}{3}\]
Putting the x on the left side and multiplying by 3 to get:
\[3y-5x=-44\]

Answer 11

y = ax + b -3 = 7a + b b = -7a - 3 and -8 = 4a + b b = -4a - 8 then -7a - 3 = -4a - 8 3a = 5 a = 5/3 b = - 4(5/3) - 8 b = - 20/3 - 24/3 = -44/3 y = (5/3)x - 44/3 3y = 5x - 44 5x - 3y = 44