Question 223752
how do i find the equation for 3/4 (6,-1)


Here, I assume you meant the slope is {{{3/4}}} passing through the point (6,-1)


Write an equation for the line described as slope {{{m=3/4}}} and passes through (6,-1). Write equation 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=3/4.


Step 2.  The slope m is given as


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


Step 3.  Let (x1,y1)=(6,-1) or x1=6 and y1=-1.  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.


Step 4.  Now we're given {{{m=3/4}}}.  Substituting above values and variables in the slope equation m yields the following steps:


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


{{{3/4=(y-(-1))/(x-6)}}}


Step 5.  Multiply (x-6) to both sides to get rid of denominators on both sides of equation.


{{{(x-8)*(3/4)=(x-6)(y+1)/(x-6)}}} 


{{{3x/4-8*3/4=y+1}}}


{{{3x/4-6=y+1}}} 


Step 6.  Now add -1 to both sides of equation to solve for y.


{{{3x/4-6+(-1)=y+1+(-1)}}} 


{{{3x/4-7=y}}}



Step 7.  ANSWER:  The equation is {{{y=3x/4-7}}}


Here's a graph below and note the slope and y-intercept at x=0  or point (0,-7) and the x-intercept at y=0 or at point (51/3, 0)and note it is consistent with the equation when substituting these 


{{{graph(500,500, -10,20,-15,5, 3x/4-7)}}}


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