Question 218678
Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope.


Point (3,5) Slope m=3/5


Step 1.  The slope m is given as


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


Step 2.  Let (x1,y1)=(3,5) or x1=3 and y1=5 .  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.


Step 3.  Now we're given {{{m=3/5}}}.  Substituting above values and variables in the slope equation m yields the following steps:


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


{{{3/5=(y-5)/(x-3)}}}


Step 4.  Multiply (x-3) to both sides to get rid of denominators 


{{{3/5*(x-3)=(x-3)(y-5)/(x-3)}}} 


{{{3x/5-9/5=y-5}}} 


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


{{{3x/5-9/5+5=y-5+5}}}


{{{3x/5-16/5=y}}}


Note:  the above equation can be rewritten as 

{{{3x-5y=16}}}

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


*[invoke describe_linear_equation 3, -5, 16]



I hope the above steps were helpful.


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Respectfully,
Dr J

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