Question

If the slope of the line joining the points (3,-6), and (-6, 3) is equal to the slope of the
line joining (3, x) and (x², -3), then find the value of x
of the straight line.
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Answer 1

Answer:

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Answer 2

Answer:

The value of x = 3, -2

Step-by-step explanation:

Given

The slope of the line joining  points (3,-6), and (-6, 3) is equal to the slope of the line joining (3, x) and (x², -3),

To find,

The value  of 'x'

Recall the formula,

The slope of the line joining two points (x₁, y₁) and (x₂,y₂) is given by

$\frac{y_2 - y_1}{x_2 - x_1}$

Solution:

The slope of the line joining the points (3,-6), and (-6, 3)

= $\frac{3 - 6}{-6 - 3}$ = -1

The slope of the line joining the points (3, x) and (x², -3)

= $\frac{-3-x}{x^2 - 3}$

Since it is given that the slopes of the two lines are equal we have

-1 = $\frac{-3-x}{x^2 - 3}$

-1(x² - 3) = -3-x

-x² + 3 = -3 -x

-x² + 3 = -3 -x

-x² + x + 6 = 0

x² - x - 6 = 0

(x-3)(x+2) = 0

x = 3, x = -2

Answer:

The value of x = 3, -2

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