SOLUTION: Write the slope intercept form of the equation of the line through the given point with the given slope. through:(3,-1), slope=-1

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Question 224826: Write the slope intercept form of the equation of the line through the given point with the given slope.
through:(3,-1), slope=-1
Found 2 solutions by drj, LtAurora:
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 through the given point with the given slope.
through:(3,-1), 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 (3,-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)=(3,-1) or x1=3 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. Substituting above values and variables in the slope equation m yields the following steps:

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

-1=%28y-%28-1%29%29%2F%28x-3%29=%28y%2B1%29%2F%28x-3%29

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

-%28x-3%29=y%2B1

-x%2B3=y%2B1

Step 7. Add -1 to both sides of the equation

-x%2B3%2B%28-1%29=y%2B1%2B%28-1%29

-x%2B2=y

Step 7. ANSWER: The equation in slope-intercept form is y=-x%2B2 where the slope m=-1 and the y-intercept b=2.

Note: the above equation can be rewritten in standard form as

x%2By=2

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+1+y+=+2 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-1%2F1.
  • 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.
graph%28+500%2C+500%2C+2-8%2C+2%2B8%2C+2-8%2C+2%2B8%2C+-1%2Ax%2B2+%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

Answer by LtAurora(115) About Me  (Show Source):
You can put this solution on YOUR website!
We have to use this equation:
%28y-y_1%29=m%28x-x_1%29
So, our y_1=-1, x_1=3, m=-1.
%28y-%28-1%29%29=-1%2A%28x-3%29
Which simplifying a bit gives us:
y%2B1=-x%2B3
So, move the 1 to the other side by subtracting from both:
y=-x%2B2
And that's our answer.