SOLUTION: Find the equation of the line containing the point (8, –39) and parallel to the line 6x+y= -4 .

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Question 225969: Find the equation of the line containing the point (8, –39) and parallel to the line 6x+y= -4 .

Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
Find the equation of the line containing the point (8, –39) and parallel to the line 6x+y= -4 .

Step 1. We can find the slope by recognizing that parallel lines have the same slope. So we need to put the equation of the line in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept b when x=0 or at point (0,b).
We can transform the given equation by subtracting -6x from both sides of the equation



Since is in slope-intercept form given as y=mx+b where the slope m=-6 and the y-intercept b=-4 when x=0 or at point (0,b) or (0,-4).

Step 2. Now we have to find the line with slope m=-6 going through point (8,-39).

Step 3. Given two points (x1,y1) and (x2,y2), then the slope m is given as



Step 4. Let (x1,y1)=(8,-39) or x1=8 and y1=-39. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given . Substituting above values and variables in the slope equation m yields the following steps:





Step 6. Multiply x-8 to both sides to get rid of denominator on right side of equation.





Subtract 39 from both sides of the equation





Step 7. ANSWER: The equation in slope-intercept form is


Note: the above equation can be rewritten as



And the graph is shown below which is consistent with the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 9/6 = 1.5.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 9/1 = 9.
  • Slope is -6/1 = -6.
  • Equation in slope-intercept form: y=-6*x+9.



I hope the above steps and explanation were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV
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