Question 224221
Write the slope intercept form of the equation of the line through the given point with the given slope.

through: (-2,5), slope=-4


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 1.  The slope m is given as


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


Step 2.  Let (x1,y1)=(-2,5) or x1=2 and y1=1 .  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.


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


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


{{{-4=(y-5)/(x-(-2))}}}


{{{-4=(y-5)/(x+2)}}}


Step 4.  Multiply x+2 to both sides to get rid of denominator on right side of equation.


{{{-4(x+2)=y-5}}} 


{{{-4x-8=y-5}}} 


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


{{{-4x-8+5=y-5+5}}}


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


Note:  the above equation can be rewritten as 


{{{4x+y=-3}}}


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


*[invoke describe_linear_equation 4, 1, -3 ]



I hope the above steps and explanation were helpful.


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And good luck in your studies!


Respectfully,
Dr J

http://www.FreedomUniversity.TV