SOLUTION: Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b. (6,9); x+5y=6 the equation of the line y=?

Algebra ->  Expressions-with-variables -> SOLUTION: Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b. (6,9); x+5y=6 the equation of the line y=?      Log On


   

Question 595683: Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b.
(6,9); x+5y=6
the equation of the line y=?
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b.
(6,9); x+5y=6
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Hi, there--
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Recall that parallel lines have the same slope. To solve this problem, we will rewrite the original equation in slope-intercept form to find the slope. Then we can use the point (6,9) to find the y-intercept for the parallel line. Then, presto! We'll have the equation.
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Rewrite in slope-intercept form.
x%2B5y=6
5y=-x%2B6
y=%28-1%2F5%29x%2B%286%2F5%29
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The coefficient of the x term in the slope, so the slope is -1/5. Now we will find the y-intercept. We have
y=mx%2Bb
y=-%281%2F5%29x%2Bb
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Since the point (6,9) is on this line, we can substitute these values and find out what the y-intercept has to be. In other words, we solve for b.
.
y=-%281%2F5%29x%2Bb
9=-%281%2F5%29%286%29%2Bb
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Simplify and solve for b.
9=-%286%2F5%29%2Bb
%2845%2F5%29%2B%286%2F5%29=b
b=51%2F5
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So, the equation for the parallel line in slope-intercept form is
y=-%281%2F5%29x%2B%2851%2F5%29
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The final step is to check your work to make sure you did not make a mistake.
Make sure that the point (6,9) is a solution for your equation.
y=-%281%2F5%29x%2B%2851%2F5%29
9=-%281%2F5%29%286%29%2B%2851%2F5%29
9=-%286%2F5%29%2B%2851%2F5%29
9=45%2F5
9=9
Bingo!
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A double check: I would also convert this equation to the same form as your original equation. If it is of the form, x+5y=c, you know for sure that they have the same slope.
y=-%281%2F5%29x%2B%2851%2F5%29
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Multiply every term by 5.
5y=-x%2B51
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Move x to the left side of the equation.
x%2B5y=51
Triple Bingo!!!
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That's it, the equation of your parallel line in slope-intercept form is
y=-%281%2F5%29x%2B%2851%2F5%29
.
I hope this helps! Feel free to email if any part of the explanation is unclear.
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Ms.Figgy
math.in.the.vortex@gmail.com