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

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


   

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) About Me  (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 6x%2By=-4 by subtracting -6x from both sides of the equation

y=-6x-4

Since y=-6x-4 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

m=%28y2-y1%29%2F%28x2-x1%29

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 m=-6. Substituting above values and variables in the slope equation m yields the following steps:

m=%28y2-y1%29%2F%28x2-x1%29

-6=%28y-%28-39%29%29%2F%28x-8%29=%28y%2B39%29%2F%28x-8%29

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

-6%28x-8%29%2F3=y%2B39

-6x%2B48=y%2B39

Subtract 39 from both sides of the equation

-6x%2B48-39=y%2B39-39

-6x%2B9=y

Step 7. ANSWER: The equation in slope-intercept form is y=-6x%2B9


Note: the above equation can be rewritten as

6x%2By=9

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 6+x+%2B+1+y+=+9 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-6%2F1.
  • 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.
graph%28+500%2C+500%2C+1.5-8%2C+1.5%2B8%2C+9-8%2C+9%2B8%2C+-6%2Ax%2B9+%29+



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