hey how do we convert y=mx+b to standard form?
the standard form of the equation of a straight line is usually considered to take this form
Ax + By = C, where A,B, and C are integers and A is positive.
So if your equation is in the slope-yintercept form
step 1: eliminate any fractions
step 2. "move" the x and y terms to the left, the constants to the right.
step 3: make sure the x term is positive
e.g.
y = 4/5 x -3/4
mutiply all terms by 20
20y = 16x - 15
-16x + 20 y = -15
each term times -1
16x - 20y = 15
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To convert the equation from slope-intercept form (y = mx + b) to standard form (Ax + By = C), follow these steps:
Step 1: Eliminate any fractions (if present)
If your equation has fractions, multiply all terms by the least common denominator to get rid of them. This will result in an equation with whole numbers.
Step 2: "Move" the x and y terms to the left, and the constant term to the right
In the slope-intercept form, the x and y terms are already on the left side of the equation. To move them to the left, you need to add or subtract them to both sides. Similarly, move the constant term (b) to the right side.
Step 3: Make sure the x term is positive
In the standard form, it is conventionally preferred to have the coefficient of x (A) as a positive integer. If the x term is negative, multiply the entire equation by -1 to make it positive.
Let's apply these steps to your example equation:
y = (4/5)x - 3/4
Step 1: Eliminate fractions
Multiply all terms by the least common denominator, which is 20.
20y = 16x - 15
Step 2: Move the x and y terms to the left, and the constant term to the right
-16x + 20y = -15
Step 3: Make sure the x term is positive
To make the x term positive, multiply the entire equation by -1.
16x - 20y = 15
Now, the equation is in standard form (Ax + By = C), where A = 16, B = -20, and C = 15 (integers with A as a positive value).