SOLUTION: Write the slope intercept form of the equation of the line described. through (-4,-1) parallel to y=-1/2x-1

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Question 224558: Write the slope intercept form of the equation of the line described.
through (-4,-1) parallel to y=-1/2x-1
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 (-4,-1) parallel to y=-1x/2-1

Step 1. We can find the slope by recognizing that parallel lines have the same slope. Since y=-1x%2F2-1 is in slope-intercept form given as y=mx+b where the slope m=-1/2 and the y-intercept b=-1 when x=0 or at point (0,b) or (0,-1).

Step 2. Now we have to find the line with slope m=-1/2 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=-1%2F2. Substituting above values and variables in the slope equation m yields the following steps:

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

-1%2F2=%28y-%28-1%29%29%2F%28x-%28-4%29%29=%28y%2B1%29%2F%28x%2B4%29

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

-1%28x%2B4%29%2F2=y%2B1

-1x%2F2-2=y%2B1

-1x%2F2-2=y%2B1

Step 7. Now subtract 1 form both sides of equation to solve for y.

-x%2F2-2-1=y%2B1-1

-x%2F2-3=y

Step 8. ANSWER: The equation in slope-intercept form is y=-x%2F2-3

Note: the above equation can be rewritten as

x%2B2y=-6

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 1+x+%2B+2+y+=+-6 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-1%2F2.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. -6/1 = -6.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -6/2 = -3.
  • Slope is -1/2 = -0.5.
  • Equation in slope-intercept form: y=-0.5*x+-3.
graph%28+500%2C+500%2C+-6-8%2C+-6%2B8%2C+-3-8%2C+-3%2B8%2C+-0.5%2Ax%2B-3+%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