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3 years ago

A line passes through the point (4, –3) and has slope m = 1. Find the equation in point–slope form.

Mathematics

1 answer:

timofeeve [1]3 years ago

8 0

Answer:

The expected answer is ...

y +3 = x -4

Step-by-step explanation:

The line with slope m through point (h, k) can be written in point-slope form as ...

y -k = m(x -h)

For (h, k) = (4, -3) and m=1, the filled-in form is ...

y +3 = x -4

___

It happens that the same line can be described by ...

y +4 = x -3 . . . . . matches the second choice

because that line also goes through the point (3, -4).

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Option a: $\frac{m^{5} }{162n}$ is the equivalent expression.

Explanation:

The expression is $\frac{(3m^{-2} n)^{-3}}{6mn^{-2} }$ where $m\neq 0, n\neq 0$

Let us simplify the expression, to determine which expression is equivalent from the four options.

Multiplying the powers, we get,

$\frac{3^{-3}m^{6} n^{-3}}{6mn^{-2} }$

Cancelling the like terms, we have,

$\frac{3^{-3}m^{5} n^{-1}}{6 }$

This equation can also be written as,

$\frac{m^{5}}{3^{3}6 n^{1} }$

Multiplying the terms in denominator, we have,

$\frac{m^{5} }{162n}$

Thus, the expression which is equivalent to $\frac{(3m^{-2} n)^{-3}}{6mn^{-2} }$ is $\frac{m^{5} }{162n}$

Hence, Option a is the correct answer.

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