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Let   P=(a,b )be the point of intersection of the line y=2x-10  and the line through (7,8) and (9,0) Compute a+b .

 Mar 6, 2020
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To find the equation of the line that passes through (7,8) and (9,0) 

has a slope of (0 - 8)/(9-7)  =  -8/2  =  -4

 

The equation of this line is:  y - 0  =  -4(x - 9)     --->     y  =  -4x + 36

 

Finding where these two lines intersect:  y  =  2x - 10   and   y =  -4x + 36

     --->     2x - 10  =  -4x + 36

                        6x =  46     

                         x  =  7 2/3

and                   y  =  5 1/3

 

Adding these two values give you a sum of 13.

 Mar 6, 2020

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