SOLUTION: Find the slope-intercept form of the equation of the line that passes through the given points. (2, 2) (6, -2/3)

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Question 218680: Find the slope-intercept form of the equation of the line that passes through the given points.
(2, 2)
(6, -2/3)
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find the slope-intercept form of the equation of the line that passes through the given points.

(2, 2)
(6, -2/3)

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=2, x2=6 and y2=-2/3 (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=%28-2%2F3-2%29%2F%286-2%29

m=-%288%2F3%29%2F4

m=-8%2F12=-2%2F3

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

Step 4. Now use the slope equation of step 1 and choose one of the given points. I'll choose point (2,2). 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%2F3=%28y-2%29%2F%28x-2%29

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

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


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


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


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

-2x%2F3%2B4%2F3=y-2

Add 2 from both sides of the equation

-2x%2F3%2B4%2F3%2B2=y-2%2B2

-2x%2F3%2B10%2F3=y

y=-2x%2F3%2B10%2F3 ANSWER in slope-intercept form. m=-2/3 and y-intercept b=10/3

Step 7. See if the other point (6,-2/3) or x=2 and y=0 satisfies this equation

y=-2x%2F3%2B10%2F3

-2%2F3=-2%2A6%2F3%2B2%2F3

0=0 So the point (6,-2/3) 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%2B3y=10

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+=+10 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. 10/2 = 5.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 10/3 = 3.33333333333333.
  • Slope is -2/3 = -0.666666666666667.
  • Equation in slope-intercept form: y=-0.666666666666667*x+3.33333333333333.


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.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV