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Question 224253: Write the slope intercept form of the equation of the line described.
through:(4,2), parallel to 
Found 2 solutions by drj, MathTherapy:
Answer by drj(1380)   (Show Source):
You can put this solution on YOUR website! Write the slope intercept form of the equation of the line described.
through:(4,2), parallel to 
Step 1. We can find the slope by recognizing that parallel lines have the same slope. Since is in slope-intercept form given as y=mx+b where the slope m=-3/4 and the y-intercept b=-5 when x=0 or at point (0,b) or (0,-5).
Step 2. Now we have to find the line with slope m=-3/4 going through point (4,2).
Step 3. The slope m is given as
Step 4. Let (x1,y1)=(4,2) or x1=4 and y1=2. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.
Step 5. Now we're given  . Substituting above values and variables in the slope equation m yields the following steps:
Step 6. Multiply x-4 to both sides to get rid of denominator on right side of equation.
Step 7. Now add 2 to both sides of equation to solve for y.
Note: the above equation can be rewritten as
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  describes a sloping line. For any
equation ax+by+c = 0, slope is  .- X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 20/3 = 6.66666666666667.
- Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 20/4 = 5.
- Slope is -3/4 = -0.75.
- Equation in slope-intercept form: y=-0.75*x+5.
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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
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Write the slope intercept form of the equation of the line described.
through:(4,2), parallel to 
Parallel linear equations have the same slope, and since the equation of line,  has a slope, or m of  , then the slope for the new equation will also have a slope, or m of  .
Using the point-slope formula,  , and with  , we just need to substitute these values into the point-slope formula to find the equation of the described line.
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