SOLUTION: Write an equation in standard form with integral coefficents for the line thru the point (5,3) and parallel to the line Y= -7/6x+19

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Question 215214: Write an equation in standard form with integral coefficents for the line thru the point (5,3) and parallel to the line Y= -7/6x+19
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation in standard form with integral coefficents for the line thru the point (5,3) and parallel to the line y= -7/6x+19

Step 1. An equation is in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept at point (0,b).

Step 2. Given y=-7x%2F6%2B19 has slope m=-7%2F6 and y-intercept b=19

Step 3. Parallel lines have the same slope so m=-7%2F6 for our example.

Step 4. The parallel line must pass through point (5,3) or x=5 and y=3. To find the y-intercept b for this line we use the following equation,

y=-7x%2F6%2Bb

3=-7%2A5%2F6%2Bb

3=-35%2F6%2Bb

b=%2818%2B35%29%2F6=53%2F6

Step 5. The equation for the parallel line in slope-intercept form is y=-7x%2F6%2B53%2F6

Step 6. The equation of a line in standard form is defined as Ax+By=C where A, B, and C are constants.

Step 7. To put the equation in Step 5 in standard form, multiply 6 to both sides of the equation to get

6y=-7x%2B53

Now add 7x to both sides of the equation to get it in standard form

7x%2B6y=53

Step 8. ANSWER: The equation of the parallel line is 7x%2B6y=53

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J