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


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=(y2-y1)/(x2-x1)}}}


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=(y2-y1)/(x2-x1)}}}


{{{1/2=(y-1)/(x-3))}}}


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


{{{1(x-3)/2=y-1}}} 


{{{x/2-3/2=y-1}}} 


Step 7.  Add 1 to both sides of the equation


{{{x/2-3/2+1=y-1+1}}} 


{{{x/2-1/2=y}}} 


Step 7.  ANSWER:  The equation in slope-intercept form is {{{y=x/2-1/2}}} 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+2y=-1}}}


And the graph is shown below which is consistent with the above steps.


*[invoke describe_linear_equation -1, 2, -1 ]


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