SOLUTION: Find the equation for the line with slope 1/2 and y intercept 3. Possible answers: A. x/2-y=3; B. -x+2y=6; C. x+2y=6; D. 2x-y=3

Algebra ->  Points-lines-and-rays -> SOLUTION: Find the equation for the line with slope 1/2 and y intercept 3. Possible answers: A. x/2-y=3; B. -x+2y=6; C. x+2y=6; D. 2x-y=3      Log On


   

Question 113988: Find the equation for the line with slope 1/2 and y intercept 3. Possible answers: A. x/2-y=3; B. -x+2y=6; C. x+2y=6; D. 2x-y=3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If we have a y intercept of 3, then the line goes through (0,3)



If you want to find the equation of line with a given a slope of 1%2F2 which goes through the point (0,3), you can simply use the point-slope formula to find the equation:


---Point-Slope Formula---
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is the given point

So lets use the Point-Slope Formula to find the equation of the line

y-3=%281%2F2%29%28x-0%29 Plug in m=1%2F2, x%5B1%5D=0, and y%5B1%5D=3 (these values are given)


y-3=%281%2F2%29x%2B%281%2F2%29%28-0%29 Distribute 1%2F2

y-3=%281%2F2%29x%2B0 Multiply 1%2F2 and -0 to get 0

y=%281%2F2%29x%2B0%2B3 Add 3 to both sides to isolate y

y=%281%2F2%29x%2B3 Combine like terms 0 and 3 to get 3

Now let's convert y=%281%2F2%29x%2B3 to standard form
Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)


y+=+%281%2F2%29x%2B3 Start with the given equation


2%2Ay+=+2%2A%28%281%2F2%29x%2B3%29 Multiply both sides by the LCD 2


2y+=+1x%2B6 Distribute and multiply


2y-1x+=+1x%2B6-1x Subtract 1x from both sides


-1x%2B2y+=+6 Simplify


-1%2A%28-1x%2B2y%29+=+-1%2A%286%29 Multiply both sides by -1 to make the A coefficient positive (note: this step may be optional; it will depend on your teacher and/or textbook)


1x-2y+=+-6 Distribute and simplify


The original equation y+=+%281%2F2%29x%2B3 (slope-intercept form) is equivalent to 1x-2y+=+-6 (standard form where A > 0)


The equation 1x-2y+=+-6 is in the form Ax%2BBy+=+C where A+=+1, B+=+-2 and C+=+-6





So the answer is B)