SOLUTION: Find the slope of a line passing through the points (1,3) and (2,5)?

Algebra ->  Linear-equations -> SOLUTION: Find the slope of a line passing through the points (1,3) and (2,5)?      Log On


   

Question 218612: Find the slope of a line passing through the points (1,3) and (2,5)?
Found 2 solutions by rfer, drj:
Answer by rfer(16322) About Me  (Show Source):
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find the slope of a line passing through the points (1,3) and (2,5)?

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=1, y1=3, x2=2 and y2=5 (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=%285-3%29%2F%282-1%29

m=2%2F1

m=2

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

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

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


+2=%28y-3%29%2F%28x-1%29

+2=%28y-3%29%2F%28x-1%29

Step 5. Multiply both sides of equation by x-1 to get rid of denomination found on the right side of the equation


+2%28x-1%29=%28x-1%29%28y-3%29%2F%28x-1%29


+2%28x-1%29=y-3


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

2x-2=y-3

Add 2 from both sides of the equation

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

2x%2B1=y

y=2x%2B1 ANSWER in slope-intercept form. m=2 and y-intercept b=1

Step 7. See if the other point (2,5) or x=2 and y=5 satisfies this equation

y=2x%2B1

5=2%2A2%2B1

5=5...a true statement. So the point (2,5) 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%2By=1

See graph below to check the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -2+x+%2B+1+y+=+1 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--2%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 1/-2 = -0.5.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 1/1 = 1.
  • Slope is --2/1 = 2.
  • Equation in slope-intercept form: y=2*x+1.
graph%28+500%2C+500%2C+-0.5-8%2C+-0.5%2B8%2C+1-8%2C+1%2B8%2C+2%2Ax%2B1+%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