SOLUTION: Wath is the slope of the line passing through (-5,5) and (9,-9)

Algebra ->  Linear-equations -> SOLUTION: Wath is the slope of the line passing through (-5,5) and (9,-9)      Log On


   

Question 226311: Wath is the slope of the line passing through (-5,5) and (9,-9)
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Wath is the slope of the line passing through (-5,5) and (9,-9)

Step 1. We will put the equation of the line in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).

Step 2. The slope of the line m is given as

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

where for our example is x1=-5, y1=5, x2=9 and y2=-9 (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 3. Substituting the above values in the slope equation gives

m=%28-9-5%29%2F%289-%28-5%29%29

m=-14%2F14=-1

Step 4. The slope is calculated as -1 or m=-1

Step 5. Now use the slope equation of Step 2 and choose one of the given points. I'll choose point (-5,5). Letting y=y2 and x=x2 and substituting m=-1 in the slope equation given as,

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


+-1=%28y-5%29%2F%28x-%28-5%29%29

-1=%28y-5%29%2F%28x%2B5%29

Step 6. Multiply both sides of equation by x+5 to get rid of denomination found on the right side of the equation


-%28x%2B5%29=%28x%2B5%29%28y-5%29%2F%28x%2B5%29


+-%28x%2B5%29=y-5


Step 7. Now simplify and put the above equation into slope-intercept form.

-x-5=y-5

Add 5 from both sides of the equation

-x-5%2B5=y-5%2B5

-x=y

y=-x This is in slope-intercept form where the slope m=-1 and y-intercept b=0

Step 8. See if the other point (9,-9) or x=9 and y=-9 satisfies this equation

y=-x

-9=-9 which is true

So the point (9,-9) satisfies the equation and is on the line. In other words, you can use the other point to check your work.

Step 9. ANSWER: The equation of the line is y=-x

Note: above equation can be also be transform into standard form as

x%2By=0

See graph below to check the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 1+x+%2B+1+y+=+0 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-1%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 0/1 = 0.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 0/1 = 0.
  • Slope is -1/1 = -1.
  • Equation in slope-intercept form: y=-1*x+0.
graph%28+500%2C+500%2C+0-8%2C+0%2B8%2C+0-8%2C+0%2B8%2C+-1%2Ax%2B0+%29+



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.

Good luck in your studies!

Respectfully,
Dr J