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3 years ago

What is the slope of the line passing through the points (2, −5) and (4, 1)?

Mathematics

1 answer:

Yuri [45]3 years ago

8 0

Slope =change of y over change of x

(2, −5) and (4, 1)

M= 1-(-5)/4-2

M=6/2

M=3

So the slope is 3.

If you need the equation

Y=mx+b

(4, 1)

1= 3(4)+b

1=12+b

1-12=b

-11=b

So equation

Y=3x-11

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1 year ago

What is the equation of the line that has a slope of -6 and passes through the point (-1,3)

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2 years ago

Solving Rational Inequalities and use sign diagram to sketch the graph. Image attached for better understanding.

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Answer:

x ∈ (-∞, -1) ∪ (1, ∞)

Step-by-step explanation:

To solve this problem we must factor the expression that is shown in the denominator of the inequality.

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$x ^ 2-1 = 0\\x ^ 2 = 1$

So the roots are:

$x = 1\\x = -1$

Therefore we can write the expression in the following way:

$x ^ 2-1 = (x-1)(x + 1)$

Now the expression is as follows:

$\frac{(x-2) ^ 2}{(x-1) (x + 1)}\geq0$

Now we use the study of signs to solve this inequality.

We have 3 roots for the polynomials that make up the expression:

$x = 1\\x = -1\\x = 2$

We know that the first two are not allowed because they make the denominator zero.

Observe the attached image.

Note that:

$(x-1)\geq0$ when $x\geq-1$

$(x + 1)\geq0$ when $x\geq1$

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$(x-2) ^ 2$ is always $\geq0$

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This is the same as

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