Q:

Write the standard form of the line that passes through the point (-2, 4) and is parallel to x - 2y = 6. Type your answer in the box provided or use the upload option to submit your solution.Please explain how you got the answer

Accepted Solution

A:
The line x - 2y = 6 we can find the slope of by solving for y

x - 2y = 6
-2y = -x + 6 --- subtract 6 from both sides
y = (-x + 6)/-2 --- divide both sides by -2
y = x/2 - 3

x/2 is equivalent to 1/2 * x.
this is in y = mx + b form where m is the slope, so the slope should be 1/2.

lines are parallel if their slopes are the same.
so the slope passing through
(-2, 4) should also have a slope of 1/2.

use point-slope form with (x1,y1) = (-2,4) and slope = 1/2

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

standard form is Ax+By + C where A and B are not decimals.
put x and y together

y - 4 = 1/2x + 1
- 4 = 1/2x - y + 1 ----subtract y from both sides
- 5 = 1/2x - y -----subtract 1 from boths sides

multiply both sides by 2

-10 = x - 2y

so the standard form is x - 2y = -10.
also y u no reply to dms