Question 224990
Find the slope intercept equation of the line that has the given characteristics


slope 4 and y intercept (0,3)


slope intercept equation is y=4x+3


Step 1. The equation in 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).  

In your example we compare y=mx+b such that m=4 and b=3.  Therefore, y=4x+3.


Step 2.  Here's another way...now we have to find the line with slope m=4 going through point (0,3).


Step 3.  Given two points (x1,y1) and (x2,y2), then the slope m is given as


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


Step 4.  Let (x1,y1)=(0,3) or x1=0 and y1=3.  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.


Step 5.  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-3)/(x-0))}}}


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


Step 6.  Multiply x to both sides to get rid of denominator on right side of equation.


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


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


Step 7.  Add 3 to both sides of the equation


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


{{{4x+3=y}}} same as in Step 1.


Step 7.  ANSWER:  The equation in slope-intercept form is {{{y=4x+3}}} where the slope m=7 and the y-intercept b=-5.


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


{{{-7x+y=-5}}}


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


*[invoke describe_linear_equation -7, 1, -5 ]


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