Which shows how to use similar right triangles to find the equation of the line through (0,6) and any point (x,y), on the line?

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03-11-2022
Mathematics

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Which shows how to use similar right triangles to find the equation of the line through (0,6) and any point (x,y), on the line?

Sagot :

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FrederickN384637 FrederickN384637 · Answer 1 · 2022-11-03T07:21:54-04:00

By the given triangles in the figure, you can notice that the following proportion must be equal, because the involved sides are congruent:

[tex]\frac{y-b}{x-0}=\frac{m+b-b}{1-0}[/tex]

In the left side, side of triangle with length y - b, divided by side with length x, must be equal to the quotient between side with length m + b - b and side with length 1.

Solve the previous equation for y, just as follow:

[tex]\begin{gathered} \frac{y-b}{x}=m \\ y-b=mx \\ y=mx+b \end{gathered}[/tex]

Sagot :

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