How would i convert a point slope form equation to slope intercept(y=mx+b) with a fraction

Question

example - y - 6 = -1/2 (x-3)

Answer 1

As is often the case in life, there can be more than one way to tackle a problem. Misha's way of starting by distributing the times-(-¹/₂) is obviously an effective way to convert from a point-slope form of an equation to a point-intercept form.

The way I'm going to show her minimizes the use of fraction arithmetic.

Starting with our equation:

. y - 6 = -¹/₂ (x - 3)

let's eliminate our fraction by multiplying both sides of the equation by 2...

. 2 [y - 6] = 2 [-¹/₂ (x - 3) ]

Now, distribute the times-2 on the left side and let the 2 times the -¹/₂ on the right side of the equation...

. 2y - 12 = -1 (x - 3)

Now distribute the times-(-1) on the right side of the equation...

. 2y - 12 = -x + 3

Eliminate the minus-12 on the left side by adding 12 to both sides...

2y - 12 + 12 = -x + 3 + 12

. 2y = -x + 15

now multiply both sides by ¹/₂ to change the 2y to y...

. ¹/₂ * ( 2y ) = ¹/₂ * (-x + 15)

Multiply the ¹/₂ and the 2 on the left side and distribute the times-¹/₂ on the right side...

. y = -¹/₂ x + ¹⁵/₂

Because the final answer contains a fraction, there's no way to fully eliminate the use of fractions, but this way eliminates the use of fractions in the early part of the problem. Bottom line, use the way that most appeals to you.

Answer 2

y - 6 = -1/2 (x-3)

First distribute the -1/2

y-6= (-1/2)x+3/2

Then add the 6 to both sides

y=(-1/2)x+6+3/2

Combine the two numbers by finding common denominator which would be 2

6=12/2

Add 12/2 + 3/2 = 15/2

Final answer is

y=(-1/2)x+15/2