Question 224830
Write the slope intercept form of the equation of the line through the given point with the given slope.

through:(-1,2), slope=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=2 going through point (-1,2).


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)=(-1,2) or x1=-1 and y1=2.  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.


Step 5.  Now we're given {{{m=2}}}.  Substituting above values and variables in the slope equation m yields the following steps:


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


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


Step 6.  Multiply x-1 to both sides to get rid of denominator on right side of equation.


{{{2(x+1)=y-2}}} 


{{{2x+2=y-2}}} 


Step 7.  Add 2 to both sides of the equation


{{{2x+2+2=y-2+2}}} 


{{{2x+4=y}}} 


Step 7.  ANSWER:  The equation in slope-intercept form is {{{y=2x+4}}} where the slope m=2 and the y-intercept b=4.


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


{{{-2x+y=4}}}


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


*[invoke describe_linear_equation -2, 1, 4 ]


I hope the above steps and explanation were helpful.


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And good luck in your studies!


Respectfully,
Dr J

http://www.FreedomUniversity.TV