solve y-4=1/2(x+3) in standard form and slope-intercept showing work?

Answer 1

A reminder that slope-intercept form looks like this:

y = mx + b

And that standard form looks like this:

Ax + By + C = 0 (for A positive)

Let's first solve the problem in slope-intercept form.

y - 4 = (1/2)(x + 3)

First, let's distribute the 1/2

y - 4 = (1/2)x + 3/2

Now, let's bring the -4 over to the right hand side.

y = (1/2)x + 3/2 + 4

Let's change 4 into a fraction over 2.

y = (1/2)x + 3/2 + 8/2
y = (1/2)x + 11/2

That is clearly in slope-intercept form (y = mx + b, as we can identify our m and our b).

To change it to standard form, let's revert back to the original question.

y - 4 = (1/2) (x + 3)

Multiply both sides by 2, to get rid of the fraction.

2(y - 4) = x + 3

And then multiply the 2 out

2y - 8 = x + 3

Now, bring everything over to the right hand side.

0 = x + 3 - 2y + 8

And then combine like-terms, and rearrange.

0 = x - 2y + 11

Therefore, x - 2y + 11 = 0 is clearly in standard form (Ax + By + C = 0).

Answer 2

Slope intercept form:
y=mx+b
y-4=1/2x+3/2
y=1/2x+3/2+8/2
y=1/2x+11/2

Standard form:
Ax+By=C

Multiply 2 on both sides:
2y=x+11

Subtract x from both sides:
-x+2y=11

Answer 3

y-4=1/2(x+3)
y-4=1/2x+3/2
y=1/2x11/2 --> slope-intercept form
-1/2x+y=11/2
-x+2y=11
x-2y=-11 --> standard form

Answer 4

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