SOLUTION: Please help me graph the line containing the given pair of points & find the slope (2,0), (-3,-2) *type integer or simplified fraction*

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Question 223788: Please help me graph the line containing the given pair of points & find the slope (2,0), (-3,-2)
*type integer or simplified fraction*
Found 2 solutions by checkley77, drj:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(2,0), (-3,-2)
Slope=(y2-y1)/(x1-x2)
Slope=(-2+0)/(-3-2)=-2/-5=2/5 for the slope.
Y=mX+b
0=2/5*2+b
0=4/5+b
b=-4/5 the y intercept.
Y=2x/5-4/5
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+2x%2F5+-4%2F5%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, 2x/5 -4/5).

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me graph the line containing the given pair of points & find the slope (2,0), (-3,-2)

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=0, x2=-3 and y2=-2 (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=%28-2-0%29%2F%28-3-2%29

m=-2%2F-5

m=2%2F5

Step 3. The slope is calculated as 2/5 or m=2%2F5

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=-3 in the slope equation given as,

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


+2%2F5=%28y-%28-2%29%29%2F%28x-%28-3%29%29

+2%2F5=%28y%2B2%29%2F%28x%2B3%29

Step 5. Multiply both sides of equation by (x+3) to get rid of denomination found on the right side of the equation


+2%28x%2B3%29%2F5=%28x%2B3%29%28y%2B2%29%2F%28x%2B3%29


+2%28x%2B3%29%2F5=y%2B2


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

2x%2F5%2B6%2F5=y%2B2

Subtract 2 from both sides of the equation

2x%2F5%2B6%2F5-2=y%2B2-2

2x%2F5-4%2F5=y

y=2x%2F5-4%2F5 ANSWER in slope-intercept form. m=2/5 and y-intercept=-4/5

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

y=2x%2F5-4%2F5

0=2%2A2%2F5-4%2F5

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-5y=4

See graph below to check the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 2+x+%2B+-5+y+=+4 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-2%2F-5.
  • 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/-5 = -0.8.
  • Slope is -2/-5 = 0.4.
  • Equation in slope-intercept form: y=0.4*x+-0.8.
graph%28+500%2C+500%2C+2-8%2C+2%2B8%2C+-0.8-8%2C+-0.8%2B8%2C+0.4%2Ax%2B-0.8+%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