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Determine x so that the three points (x, -3), (9, 1) and (13, 2) will lie in a straight line

Sagot :

Given,
[tex]P_1(13,2)[/tex]
[tex]P_2(9,1)[/tex]
[tex]P_3(x,-3)[/tex]

Formula:

[tex]m= \frac{y_2-y_1}{x_2-x_1} [/tex]

solution:

First get the slope from [tex]P_1[/tex] to [tex]P_2[/tex]

[tex]m= \frac{1-2}{9-13} [/tex]

[tex]m= \frac{1}{4} [/tex]

then, solve for the x:

[tex]m= \frac{-3-1}{x-9} [/tex]

[tex]\frac{1}{4}= \frac{-3-1}{x-9} [/tex]

[tex]x-9=4(-3-1)[/tex]

[tex]x=-7[/tex]

checking 

[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_2}{x_3-x_2}[/tex]

[tex] \frac{1}{4} = \frac{-3-1}{-7-9} [/tex]

[tex] \frac{1}{4} = \frac{1}{4} [/tex]