SOLUTION: find an equation of the line containg the given pair of points (-2,-9) and (-6,-4)

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Question 220921: find an equation of the line containg the given pair of points (-2,-9) and (-6,-4)
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation of the line containg the given pair of points (-2,-9) and (-6,-4)

However, here are the steps showing you how you can check your work with one of the points.

Step 1. The slope of the line m is given as

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

where for our example is x1=-2, y1=-9, x2=-6 and y2=-4 (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 2. Substituting the above values in the slope equation gives

m=%28-4-%28-9%29%29%2F%28-6-%28-2%29%29

m=-5%2F4

Step 3. The slope is calculated as -5/4 or m=-5/4

Step 4. Now use the slope equation of step 1 and choose one of the given points. I'll choose point (-2, -9). Letting y=y2 and x=x2 and substituting m=-3 in the slope equation given as,

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


+-5%2F4=%28y-%28-9%29%29%2F%28x-%28-2%29%29

+-5%2F4=%28y%2B9%29%2F%28x%2B2%29

Step 5. Multiply both sides of equation by x+2 to get rid of denomination found on the right side of the equation


+%28-5%2F4%29%28x%2B2%29=%28x%2B2%29%28y%2B9%29%2F%28x%2B2%29


+-%285%2F4%29%28x%2B2%29=y%2B9


Step 6. Now simplify and put the above equation into slope-intercept form.

-5x%2F4-5%2F2=y%2B9

Subtract 9 from both sides of the equation

-5x%2F4-5%2F2-9=y%2B9-9

-5x%2F4-23%2F2=y

y=-5x%2F4-23%2F2 ANSWER in slope-intercept form. m=-5/4 and y-intercept=-23/2

Step 7. See if the other point (-6,-4) or x=-6 and y=-4 satisfies this equation

y=-5%2A%28-6%29%2F4-23%2F2

-4=15%2F2-23%2F2

-4=-4 So the point (-6,-4) satisfies the equation and is on the line. In other words, you can use the other point to check your work.

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

5x%2B4y=-46

See graph below to check the above steps.

graph%28400%2C400%2C+-15%2C+5%2C+-15%2C+5%2C+-5x%2F4-23%2F2%29

I hope the above steps were helpful.

And good luck in your studies!

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Respectfully,
Dr J