Question

Which is an equation of an asymptote of the hyperbola? y = 3x 10 y = –3x 8 y = x 2 y = x

Answer 1

The equation of the asymptote of the hyperbola is y = 3x + 10

How to determine the asymptote?

From the complete question the asymptote passes through the points:

(x,y) = (-1, 7) and (-3,1)

The slope of the line is calculated using:

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

So, we have:

$m = \frac{7 - 1}{-1 + 3}$

This gives

m = 3

The equation is then calculated using:

y = m(x -x1) + y1

This gives

y = 3(x + 1) + 7

Evaluate

y = 3x + 3 + 7

y = 3x + 10

Hence, the equation of the asymptote is y = 3x + 10

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