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Question 224828: Write the slope intercept form of the equation of the line through the given point with the given slope.
through:(2,-4), slope=-1
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 through the given point with the given slope.
through:(2,-4), slope=-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).
Step 2. Now we have to find the line with slope m=-1 going through point (2,-4).
Step 3. Given two points (x1,y1) and (x2,y2), then the slope m is given as
Step 4. Let (x1,y1)=(2,-4) or x1=2 and y1=-4. 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-1 to both sides to get rid of denominator on right side of equation.
Step 7. Add -4 to both sides of the equation
Step 7. ANSWER: The equation in slope-intercept form is  where the slope m=-1 and the y-intercept b=-2.
Note: the above equation can be rewritten in standard form 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. -2/1 = -2.
- Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -2/1 = -2.
- Slope is -1/1 = -1.
- Equation in slope-intercept form: y=-1*x+-2.
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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
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