The line through (1, 3) with slope of 1/2 (I used the point slope equation)
y-y1 = m(x-x1) y-3 = 1/2(x-1)
(work the parenthesis first)
Y-3=1/2x-1/2
+3 +3
Y = 1/2x+5/2 LCD of 2 to convert fractions into whole numbers.
2y = x+5 Answer, however I need to place it in standard form where x and y are on the same side.
2y = x+5
-x -x
-x+2y=5 This should be the correct and final answer
Choices below are from the textbook, but none of the answers I come up with match any of the choices. What did I do wrong, and would you show me the steps as I have to show my work, and I can see where I made my mistake? Thanks
x+4y =13
x=1
x-2y = 5
y = 8x-5
y = 2x+1
y = 3
2x+y=5
3x+4y=15
From your Y-3=1/2x-1/2 , I would multiply each term by 2
2y - 6 = x - 1
-x + 2y = 5
x - 2y = -5
the slope of this line is 1/2
and the point (1,3) satisfies it.
Your derivation is so full of errors that I cannot follow it at all. Most steps do not follow from the previous step.
The first thing to write down is
y - 3 = (1/2)(x - 1)
from which follows:
y = x/2 + 3 - 1/2 , and
= x/2 + 5/2
That would be the standard "y = mx + b" frm
If you want x and y on the same side,
y - x/2 = 5/2 or
2y - x = 5
To find the equation of a line with a given slope and passing through a given point, you correctly started with the point-slope equation:
y - y1 = m(x - x1)
Where (x1, y1) is the given point and m is the slope.
In your case, (x1, y1) = (1, 3) and m = 1/2. So, substituting these values into the point-slope equation, you correctly obtained:
y - 3 = 1/2(x - 1)
Next, you distributed the 1/2 to the terms inside the parentheses:
y - 3 = 1/2x - 1/2
Then, you added 3 to both sides to isolate y:
y = 1/2x - 1/2 + 3
Simplifying, you combined the 3 and -1/2:
y = 1/2x - 1/2 + 6/2
This becomes:
y = 1/2x + 5/2
At this point, your equation is correct, but if you need to put it in standard form where x and y are on the same side, you need to move the x term to the left side. Here's how you can do that:
Start with the equation:
y = 1/2x + 5/2
Multiply through by 2 to eliminate the fractions:
2y = x + 5
Now, move the x term to the left side by subtracting x from both sides:
2y - x = 5
This is the final equation in standard form.
Now, let's compare this with the given choices:
- x + 4y = 13: Not a match
- x = 1: Not relevant
- x - 2y = 5: Not a match
- y = 8x - 5: Not a match
- y = 2x + 1: Not a match
- y = 3: Not a match
- 2x + y = 5: Not a match
- 3x + 4y = 15: Not a match
None of the provided choices match the equation you derived. It's possible that there was an error in the textbook's options or that there was a mistake in the given information. However, the equation you obtained, 2y - x = 5, is correct based on the given slope and point.