SOLUTION: given two lines: l1 x+2y=4 and l2 3x-y=5, write the equation of line l such that l is perpendicular to l1, and l has the same y-intercept as l2.

Question 206053: given two lines: l1 x+2y=4 and l2 3x-y=5, write the equation of line l such that l is perpendicular to l1, and l has the same y-intercept as l2.
Found 2 solutions by HyperBrain, MathTherapy:
Answer by HyperBrain(694) (Show Source): You can put this solution on YOUR website!
Two lines with slopes m and n are perpendicular if and only if mn=-1. so, n=-1/m
line 1: x+2y=4
**
2y=-x+4 [its slope is -1]
***
line 2: 3x-y=5
**
y=3x-5 [its y intercept is -5]
{}{}{}{
Now, since line 1 has slope -1, the required line has slope n=-1/-1=1
+++
Therefore, the equation of the required line is y=x-5
Power up,
HyperBrain!
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

given two lines: l1 x+2y=4 and l2 3x-y=5, write the equation of line l such that l is perpendicular to l1, and l has the same y-intercept as l2.

L1 -----> x + 2y = 4 -----> 2y = -x + 4
Therefore, L1, in y = mx + b form is:

Therefore, L1's slope is , meaning that its perependicular equation

will have a slope of 2.

Now, L2 -----> 3x - y = 5 -----> -y = -3x + 5
Therefore, L2, in y = mx + b form is:

Therefore, L2's y-intercept is - 5.

Therefore, the equation that is perependicular to x + 2y = 4, and that has the

same y-intercept as 3x - y = 5, in y = mx + b form, is: , and in standard form:
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