SOLUTION: Write the slope intercept form of the equation of the line through the given point with the given slope. through:(3,5), slope=5/3

Algebra ->  Linear-equations -> SOLUTION: Write the slope intercept form of the equation of the line through the given point with the given slope. through:(3,5), slope=5/3      Log On


   

Question 224827: Write the slope intercept form of the equation of the line through the given point with the given slope.
through:(3,5), slope=5/3
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Write the slope intercept form of the equation of the line through the given point with the given slope.
through:(3,5), slope=5/3

Step 1. The slope-intercept form is 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. Now we have to find the line with slope m=5/3 going through point (3,5).

Step 3. Given two points (x1,y1) and (x2,y2), then the slope m is given as

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

Step 4. Let (x1,y1)=(3,5) or x1=3 and y1=5. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given m=5%2F3. Substituting above values and variables in the slope equation m yields the following steps:

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

5%2F3=%28y-5%29%2F%28x-3%29

Step 6. Multiply x-3 to both sides to get rid of denominator on right side of equation.

5%28x-3%29%2F3=y-5

5x%2F3-5=y-5

Step 7. Add 5 to both sides of the equation

7x-5%2B5=y-5%2B5

5x%2F3=y

Step 7. ANSWER: The equation in slope-intercept form is y=5x%2F3 where the slope m=5/3 and the y-intercept b=0.

Note: the above equation can be rewritten in standard form as

-5x%2B3y=0

And the graph is shown below which is consistent with the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -5+x+%2B+3+y+=+0 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--5%2F3.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 0/-5 = 0.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 0/3 = 0.
  • Slope is --5/3 = 1.66666666666667.
  • Equation in slope-intercept form: y=1.66666666666667*x+0.
graph%28+500%2C+500%2C+0-8%2C+0%2B8%2C+0-8%2C+0%2B8%2C+1.66666666666667%2Ax%2B0+%29+



I hope the above steps and explanation 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