SOLUTION: Find The Equation Of The Line That Passes Through (4,6) And Is Parallel To The Line That Passes Through (6,-6) And (10,-4)?

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Question 225491: Find The Equation Of The Line That Passes Through (4,6) And Is Parallel To The Line That Passes Through (6,-6) And (10,-4)?
Found 2 solutions by drj, solver91311:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find The Equation Of The Line That Passes Through (4,6) And Is Parallel To The Line That Passes Through (6,-6) And (10,-4)?

Step 1. We'll put the equation of the line in slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b). Also we know that parallel lines have the same slope. So let's find the slope of the line passing through the point (6,-6) and (10,-4)

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

m=%28y2-y1%29%2F%28x2-x1%29=%28-4-%28-6%29%29%2F%2810-6%29=2%2F4=1%2F2

Step 2. Now we have to find the line with slope m=1%2F2 going through point (4,6).

Step 3. As mentioned earlier, 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)=(4,6) or x1=4 and y1=6. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given m=1%2F2. Substituting above values and variables in the slope equation m yields the following steps:

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

1%2F2=%28y-6%29%2F%28x-4%29

Step 6. Multiply x-4 to both sides to get rid of denominator on right side of equation.

%28x-4%29%2F2=y-6

x%2F2-2=y-6

Step 7. Add 6 to both sides of the equation

x%2F2-2%2B6=y-6%2B6

x%2F2%2B4=y

Step 7. ANSWER: The equation in slope-intercept form is y=x%2F2%2B4 where the slope m=1%2F2 and the y-intercept b=4.

Note: the above equation can be rewritten in standard form as

-x%2B2y=8

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 -1+x+%2B+2+y+=+8 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--1%2F2.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/-1 = -8.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4.
  • Slope is --1/2 = 0.5.
  • Equation in slope-intercept form: y=0.5*x+4.
graph%28+500%2C+500%2C+-8-8%2C+-8%2B8%2C+4-8%2C+4%2B8%2C+0.5%2Ax%2B4+%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

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


First determine the slope of the line that passes through (6,-6) and (10,-4) by using the slope formula:



where and are the coordinates of the given points.

Then use the fact that parallel lines have equal slopes, or



along with the other given point and the point-slope form of the equation of a line:



where are the coordinates of the given point and is the slope you calculated in the first step.

John