SOLUTION: Write the slope intercept form of the equation of the line described. through: (-3,-3), parallel to y=7/3x+3

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Question 224549: Write the slope intercept form of the equation of the line described.
through: (-3,-3), parallel to y=7/3x+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 described.
through: (-3,-3), parallel to y=7x/3+3

Step 1. We can find the slope by recognizing that parallel lines have the same slope. Since y=7x%2F3%2B3 is in slope-intercept form given as y=mx+b where the slope m=7/3 and the y-intercept b=3 when x=0 or at point (0,b) or (0,3).

Step 2. Now we have to find the line with slope m=7/3 going through point (-3,-3).

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

Step 5. Now we're given m=7%2F3. Substituting above values and variables in the slope equation m yields the following steps:

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

7%2F3=%28y-%28-3%29%29%2F%28x-%28-3%29%29=%28y%2B3%29%2F%28x%2B3%29

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

7%28x%2B3%29%2F3=y%2B3

7x%2F3%2B7%2A3%2F3=y%2B3

7x%2F3%2B7=y%2B3

Step 7. Now subtract 3 form both sides of equation to solve for y.

7x%2F3%2B7-3=y%2B3-3

7x%2F3%2B4=y

Step 8. ANSWER: The equation in slope-intercept form is y=7x%2F3%2B4


Note: the above equation can be rewritten as

-7x%2B3y=12

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 -7+x+%2B+3+y+=+12 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--7%2F3.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 12/-7 = -1.71428571428571.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 12/3 = 4.
  • Slope is --7/3 = 2.33333333333333.
  • Equation in slope-intercept form: y=2.33333333333333*x+4.




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