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

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) (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

where for our example is x1=2, y1=2, x2=6 and y2=-2/3 (think of ). 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

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,

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

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

Add 2 from both sides of the equation

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

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

See graph below to check the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .

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
RELATED QUESTIONS
Find the slope-intercept form of the equation of the line that passes through the given... (answered by drj)

Find the equation, in slope-intercept form, of the line that passes through the points... (answered by josmiceli)

. Find the equation, in slope-intercept form, of the line that passes through the points (answered by tutorcecilia)

Find the equation of a line in slope-intercept form that passes through the points (-2,... (answered by rothauserc)

Find the equation, in slope-intercept form, of the line that passes through the points... (answered by josmiceli)

Find the equation, in slope-intercept form, of the line that passes through the points... (answered by Mathtut)

Find the equation, in slope-intercept form, of the line that passes through the points... (answered by jim_thompson5910)