Question 217758
Write an equation for the line described as slope=-3/5 and passes through (7,6). Write in slope intercept form.


Step 1.  The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept b at x=0 or point (0,b).  Here, the slope m=-3/5.


Step 2.  The slope m is given as


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


Step 3.  Let (x1,y1)=(6,7) or x1=7 and y1=6.  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.


Step 4.  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-6)/(x-7)}}}


Step 5.  Multiply (x-7) to both sides to get rid of denominators on both sides of equation.


{{{(x-7)*(-3/5)=(x-7)(y-6)/(x-7)}}} 


{{{-3x/5+21/5=y-6}}} 


Step 6.  Now add +6 to both sides of equation to solve for y.


{{{-3x/5+21/5+6=y-6+6}}} 


{{{-3x/5+51/5=y}}}



Step 7.  ANSWER:  The equation is {{{-3x/5+51/5=y}}}


Here's a graph below and note the slope and y-intercept at x=0  or point (0, 51/5) and the x-intercept at y=0 or at point (17, 0)and note it is consistent with the equation when substituting these 


{{{graph(500,500, -10,20,-5,15, -3x/5+51/5)}}}


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


{{{3x+5y=51}}}


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J