SOLUTION: How do I find the equation of the line which passes through the points (-3,2) and (0,4)

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Question 212931: How do I find the equation of the line which passes through the points
(-3,2) and (0,4)
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
(-3,2) and (0,4)

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 given (-3,2) and (0,4) then x1=-3, y1=2, x2=0 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=%284-2%29%2F%280-%28-3%29%29

m=2%2F3

Step 3. The slope is calculated as 2%2F3 or m=2%2F3

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

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


+2%2F3=%28y-2%29%2F%28x-%28-3%29%29

+2%2F3=%28y-2%29%2F%28x%2B3%29

Step 5. Multiply both sides of equation by x%2B3 to get rid of denominators on right side of equation.

2%28x%2B3%29%2F3=%28x%2B3%29%28y-2%29%2F%28x%2B3%29

Then multiply by 3 to get rid of denominator on left side

2%28x%2B3%29=3%28y-2%29

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

2x%2B6=3y-6

Add 6 to both sides of the equation to isolate 3y on right side

2x%2B6%2B6=3y-6%2B6

2x%2B12=3y

3y=2x%2B12

Divide 3 from both sides of equation to solve for y

3y%2F3=%282x%2B12%29%2F3

y=%282x%2F3%29%2B4 ANSWER in slope-intercept form. m=2%2F3 and y-intercept=4

Step 7. See if the other point (0,4) or x=0 and y=4 satisfies this equation

y=%282x%2F3%29%2B4

4=%282%2A0%2F3%29%2B4

4=4
So the point (0,4) 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

%28-2x%2F3%29%2By=-4

OR

-2x%2B3y=-12

See graph below to check the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -2+x+%2B+3+y+=+12 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--2%2F3.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 12/-2 = -6.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 12/3 = 4.
  • Slope is --2/3 = 0.666666666666667.
  • Equation in slope-intercept form: y=0.666666666666667*x+4.
graph%28+500%2C+500%2C+-6-8%2C+-6%2B8%2C+4-8%2C+4%2B8%2C+0.666666666666667%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