Question 224329
Find equation of the line with points m=6/7 (4,-3)


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.  The slope m is given as


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


Step 3.  Let (x1,y1)=(4, -3) or x1=4 and y1=-3 .  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.


Step 4.  Now we're given the slope {{{m=6/7}}}.  Substituting above values and variables in the slope equation m yields the following steps:


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


{{{6/7=(y-(-3))/(x-4)}}}


{{{6/7=(y+3)/(x-4)}}}


Step 5.  Multiply x-4 to both sides to get rid of denominator on right side of equation.


{{{6(x-4)/7=y+3}}} 


{{{6x/7-24/7=y+3}}} 


Step 6.  Now subtract 3 from both sides of equation to solve for y.


{{{6x/7-24/7-3=y+3-3}}}


{{{6x/7-45/7=y}}}


Note:  the above equation can be rewritten as 


{{{6x-7y=45}}}


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


*[invoke describe_linear_equation 6, -7, 45]



I hope the above steps and explanation were helpful.


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Respectfully,
Dr J

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