SOLUTION: Find an equation for the line that is described. Write the answer in the two forms y = mx + b and Ax + By + C = 0. A. Is parallel to 2x - 5y = 10 and passes through ( 1, 2)

Algebra ->  Decimal-numbers -> SOLUTION: Find an equation for the line that is described. Write the answer in the two forms y = mx + b and Ax + By + C = 0. A. Is parallel to 2x - 5y = 10 and passes through ( 1, 2)       Log On


   

Question 1207842: Find an equation for the line that is described. Write the answer in the two forms y = mx + b and Ax + By + C = 0.
A. Is parallel to 2x - 5y = 10 and passes through ( 1, 2)

B. Is parallel to 4x + 5y = 20 and passes through (0, 0)
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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A._____ Is parallel to 2x - 5y = 10 and passes through ( 1, 2)
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Parallel to Ax+By=C and passes through point (p,v)

%28-A%2FB%29x%2Bk=y

y=-%28A%2FB%29x%2Bk
-
v=-%28A%2FB%29p%2Bk

k=v%2Bp%28A%2FB%29

As the slope intercept form you would want,
y=-%28A%2FB%29x%2B%28v%2Bp%28A%2FB%29%29

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y=%282%2F5%29x%2Bk
-
k=y-2x%2F5
k=2-2%2A1%2F5
k=10%2F5-2%2F5
k=8%2F5

As slope-intercept form, equation wanted, y=%282%2F5%29x%2B8%2F5;
do what you need to for the other form desired.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The equations are both in Ax+By=C form. It's very slow and inefficient to start solving the problem by converting the given equations to slope-intercept form, as the other tutor suggested.

Given an equation in Ax+By=C form, any line parallel to it will have an equation of the form Ax+By=N for some N. Then, given a point (x,y) on the line, the value of N is determined by using those x and y values in the general form.

A. parallel to 2x-5y=10 passing through (1,2)

The equation is 2x-5y=N, where N is determined by substituting x=1 and y=2:

N = 2(1)-5(2) = 2-10 = -8

ANSWER: 2x-5y = -8

Put in slope-intercept form by solving for y:

2x-5y = -8
-5y = -2x-8
5y = 2x+8
y = (2/5)x+8/5

Solve the other one in exactly the same way.