Question 218774
Write an equation in slope-intercept form for the line that satisfies the following condition. Slope m=3 and passes through (4,20)


Step 1.  The slope m is given as


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


Step 2.  Let (x1,y1)=(4,20) or x1=4 and y1=20.  Let other point be ((x2,y2)=(x,y) or x2=x and y2=y.


Step 3.  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)}}}


{{{3=(y-20)/(x-4)}}}


Step 4.  Multiply x-4 to both sides to get rid of denominator on right side of equation.


{{{3(x-4)=y-20}}} 


{{{3x-12=y-20}}} 


Step 5.  Now add 20 to both sides of equation to solve for y.


{{{3x-12+20=y-20+20}}}


{{{3x+8=y}}}


Step 6.  ANSWER:  {{{3x+8=y}}}


Note:  the above equation can be rewritten as 

{{{3x-y=-8}}}

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


*[invoke describe_linear_equation 3, -1, -8 ]



I hope the above steps and explanation were helpful. 


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Dr J


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