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masha68 [24]
2 years ago
14

The points with coordinates (x, -1), (2,2), and (4,3) lie on the same line. What is the value of x?

Mathematics
1 answer:
borishaifa [10]2 years ago
7 0

Find the slope of the line passing throught the points (2, 2) and (4, 3).

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

Substitute:

m=\dfrac{3-2}{4-2}=\dfrac{1}{2}

If the point (x, -1) lie on the same line, then the slope of line passing through the points (2, 2) and (x, -1) the same:

Substitute:

m=\dfrac{-1-2}{x-2}=\dfrac{-3}{x-2}

We have the equation:

\dfrac{-3}{x-2}=\dfrac{1}{2}        <em>cross multiply</em>

(1)(x-2)=(-3)(2)

x-2=-6           <em>add 2 to both sides</em>

x=-4

<h3>Answer: x = -4.</h3>
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