What is the standard form of
y+2=1/2(x-4)?
a. x=2y=0
b. x-2y=8
c. 2x-y=10
d. -3x+2y=0
i honestly think it is c. its the only one that makes sense.
I appreciate trying to help, but please work out the problems to show how the answer is reached. (It also helps to check your work).
Standard form of a line is ax+by = c, with a, b, and c integers.
y+2 = (1/2)(x-4)
Distribute the (1/2).
y+2 = x/2-2
Multiply by 2 to make the coefficient of x an integer.
2y+4 = x-4
2y-x = -8
x-2y = 8
To find the standard form of the equation, we need to eliminate any fractions and rearrange the equation so that the terms with variables are on one side and the constant term is on the other side.
Given: y + 2 = (1/2)(x - 4)
First, let's distribute the (1/2) to the terms inside the parentheses:
y + 2 = (1/2)x - 2
Next, let's move the y term and the constant term to the right side:
y - (1/2)x = -2 - 2
Combining like terms:
y - (1/2)x = -4
To get rid of the fraction, we can multiply the entire equation by 2:
2(y - (1/2)x) = 2(-4)
This simplifies to:
2y - x = -8
Therefore, the standard form of the equation is:
b. x - 2y = 8
To find the standard form of the given equation, we need to rewrite it in the form Ax + By = C, where A, B, and C are integers and A is positive.
First, let's distribute 1/2 on the right side of the equation:
y + 2 = (1/2)x - 2
Simplifying further:
y = (1/2)x - 2 - 2
y = (1/2)x - 4
Next, let's get rid of the fraction by multiplying both sides of the equation by 2:
2y = x - 8
Now, let's rearrange the equation to get it in the standard form:
x - 2y = 8
So, the standard form of the equation y + 2 = (1/2)(x - 4) is option b:
x - 2y = 8