SOLUTION: write in standard form the equation of the line with slope =-2 and passing through (4,1)

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Question 225956: write in standard form the equation of the line with slope =-2 and passing through (4,1)
Answer by drj(1380) About Me  (Show Source):
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Write in standard form the equation of the line with slope =-2 and passing through (4,1)

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). Using the slope-intercept, we can translate it to the standard form given as Ax+By=C where A, B, and C are constants.

Step 2. Now we have to find the line with slope m=-2 going through point (4,1).

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)=(4,1) or x1=4 and y1=1. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

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

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

-2=%28y-1%29%2F%28x-4%29

Step 6. Multiply x-4 to both sides to get rid of denominator on right side of equation.

-2%28x-4%29=y-1

-2x%2B8=y-1

Step 7. Add 1 to both sides of the equation

-2x%2B8%2B1=y-1%2B1

-2x%2B9=y

Step 7. ANSWER: The equation in slope-intercept form is y=-2x%2B9 where the slope m=-2 and the y-intercept b=9. The above equation can be rewritten in standard form by adding 2x to both sides as 2x%2By=9.

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 2+x+%2B+1+y+=+9 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. 9/2 = 4.5.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 9/1 = 9.
  • Slope is -2/1 = -2.
  • Equation in slope-intercept form: y=-2*x+9.
graph%28+500%2C+500%2C+4.5-8%2C+4.5%2B8%2C+9-8%2C+9%2B8%2C+-2%2Ax%2B9+%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