SOLUTION: how do I find the equation of the line which passes through the points (-1,2) and (-2,0)

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Question 212929: how do I find the equation of the line which passes through the points
(-1,2) and (-2,0)
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
How do I find the equation of the line which passes through the points

(-1,2) and (-2,0)

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 (-1,2) and (-2,0) x1=-1, y1=2, x2=-2 and y2=0 (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=%280-2%29%2F%28-2-%28-1%29%29

m=-2%2F-1

m=2

Step 3. The slope is calculated as 2 or m=2

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

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


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

2=%28y-2%29%2F%28x%2B1%29

Step 5. Multiply both sides of equation by x+1 to get rid of denomination found on the right side of the equation


+2%28x%2B1%29=%28x%2B1%29%28y-2%29%2F%28x%2B1%29


2%28x%2B1%29=y-2


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

2x%2B2=y-2

Add 2 to both sides of the equation

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

2x%2B4=y

y=2x%2B4 ANSWER in slope-intercept form. m=2 and y-intercept=4

Step 7. See if the other point (-2,0) or x=-2 and y=0 satisfies this equation

y=2x%2B4

0=2%2A%28-2%29%2B4

0=0 So the point (-2,0) 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

-2x%2By=4

See graph below to check the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -2+x+%2B+1+y+=+4 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--2%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 4/-2 = -2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 4/1 = 4.
  • Slope is --2/1 = 2.
  • Equation in slope-intercept form: y=2*x+4.
graph%28+500%2C+500%2C+-2-8%2C+-2%2B8%2C+4-8%2C+4%2B8%2C+2%2Ax%2B4+%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