SOLUTION: Pleas help me solve... Find an equation of the line containing the given pair of points. (4,2), (12,6)

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Question 224547: Pleas help me solve...
Find an equation of the line containing the given pair of points. (4,2), (12,6)
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation of the line containing the given pair of points. (4,2), (12,6)

Step 1. We will 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 when x=0 or at point (0,b).

Step 2. The slope of the line m is given as

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

where for our example is x1=4, y1=2, x2=12 and y2=6 (think of slope=rise%2Frun). You can choose the points the other way around but be consistent with the x and y coordinates. You will get the same result.

Step 3. Substituting the above values in the slope equation gives

m=%286-2%29%2F%2812-4%29

m=4%2F8=1%2F2

Step 4. The slope is calculated as 1%2F2 or m=1%2F2

Step 5. Now use the slope equation of Step 2 and choose one of the given points. I'll choose point (4,2). Letting y=y2 and x=x2 and substituting m=1%2F2 in the slope equation given as,

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


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

Step 6. Multiply both sides of equation by x-4 to get rid of denomination found on the right side of the equation


+%28x-4%29%2F2=%28x-4%29%28y-2%29%2F%28x-4%29


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


Step 7. Now simplify and put the above equation into slope-intercept form.

x%2F2-4%2F2=y-2

x%2F2-2=y-2

Add 2 from both sides of the equation

x%2F2-2%2B2=y-2%2B2

x%2F2=y

y=x%2F2 This is in slope-intercept form where the slope m=1/2 and y-intercept b=0

Step 8. See if the other point (12,6) or x=12 and y=6 satisfies this equation

y=x%2F2

6=12%2F2

6=6 So the point (12,6) satisfies the equation and is on the line. In other words, you can use the other point to check your work.

Step 9. ANSWER: The equation of the line is y=x%2F2

Note: above equation can be also be transform into standard form as

-x%2B2y=0

See graph below to check the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -1+x+%2B+2+y+=+0 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. 0/-1 = 0.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 0/2 = 0.
  • Slope is --1/2 = 0.5.
  • Equation in slope-intercept form: y=0.5*x+0.
graph%28+500%2C+500%2C+0-8%2C+0%2B8%2C+0-8%2C+0%2B8%2C+0.5%2Ax%2B0+%29+



I hope the above steps 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.

Good luck in your studies!

Respectfully,
Dr J