SOLUTION: Write the slope intercept form of the equation of the line through the given point with the given slope. through(3,1), slope=1/2

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Question 224829: Write the slope intercept form of the equation of the line through the given point with the given slope.
through(3,1), slope=1/2
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=1/2

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=1/2 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=3. 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-1%29%2F%28x-3%29%29

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

1%28x-3%29%2F2=y-1

x%2F2-3%2F2=y-1

Step 7. Add 1 to both sides of the equation

x%2F2-3%2F2%2B1=y-1%2B1

x%2F2-1%2F2=y

Step 7. ANSWER: The equation in slope-intercept form is y=x%2F2-1%2F2 where the slope m=1/2 and the y-intercept b=-1/2.

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

-x%2B2y=-1

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+=+-1 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. -1/-1 = 1.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -1/2 = -0.5.
  • Slope is --1/2 = 0.5.
  • Equation in slope-intercept form: y=0.5*x+-0.5.
graph%28+500%2C+500%2C+1-8%2C+1%2B8%2C+-0.5-8%2C+-0.5%2B8%2C+0.5%2Ax%2B-0.5+%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