Question

[100POINTS)A line contains the points R (-5, -6) S (1, 5) and T (x, 10). Solve for x. Be sure to show and explain all work.

Please answer this in the most simplest way for me to understand.

Thank you.

I

Answer 1

`(41)/(11).`

Explanation:

1) to make up the equation of the given line:

`(x-X_R)/(X_S-X_R) =(y-Y_R)/(Y_S-Y_R); \ => (x+5)/(1+5) =(y+6)/(5+6); \ => (x+5)/(6) =(y+6)/(11).`

2) to substitute y=10 into the equation of the given line, then to calculate the value of 'x':

`(x+5)/(6) =(10+6)/(11); \ => \ x=(96)/(11)-5=(41)/(11).`

Answer 2

Equation of ST :-

Slope=

• m=5+6/1+5=11/6

Equation in point slope form

• y+6=11/6(x+5)
• 6y+36=11x+55
• 6y=11x+19
• y=11/6x+19/6

Now T lies on this line

• 10=11/6x+19/6

Ok solving we would get

• x=41/11