Question 225491
Find The Equation Of The Line That Passes Through (4,6) And Is Parallel To The Line That Passes Through (6,-6) And (10,-4)?


Step 1. We'll put the equation of the line 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). Also we know that parallel lines have the same slope.  So let's find the slope of the line passing through the point (6,-6) and (10,-4)


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


{{{m=(y2-y1)/(x2-x1)=(-4-(-6))/(10-6)=2/4=1/2}}}


Step 2.  Now we have to find the line with slope {{{m=1/2}}} going through point (4,6).


Step 3.  As mentioned earlier, 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)=(4,6) or x1=4 and y1=6.  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.


Step 5.  Now we're given {{{m=1/2}}}.  Substituting above values and variables in the slope equation m yields the following steps:


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


{{{1/2=(y-6)/(x-4)}}}


Step 6.  Multiply x-4 to both sides to get rid of denominator on right side of equation.


{{{(x-4)/2=y-6}}} 


{{{x/2-2=y-6}}} 


Step 7.  Add 6 to both sides of the equation


{{{x/2-2+6=y-6+6}}} 


{{{x/2+4=y}}} 


Step 7.  ANSWER:  The equation in slope-intercept form is {{{y=x/2+4}}} where the slope {{{m=1/2}}} and the y-intercept b=4.


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


{{{-x+2y=8}}}


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


*[invoke describe_linear_equation -1, 2, 8 ]


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