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2 years ago

MATH HELP FIND THE EQUATION OF THE LINE

Mathematics

2 answers:

Korolek [52]2 years ago

6 0

Hi there!

$\large\boxed{y = \frac{3}{4}x - 2}$

y = mx + b

To find the equation, we can begin by deriving the slope (m):

slope = y2-y1/x2-x1

Find two points:

(0, -2) and (4, 1)

Plug these into the slope equation:

slope = 1 - (-2) / 4 - 0

slope = 3/4

We know that there is a y-intercept of y = -2 (b value), so:

y = 3/4x - 2

Dominik [7]2 years ago

5 0

y=3/3x+-2

Step-by-step explanation:

it goes up 3 and over 3 so its 3/3 and it starts at -2

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antiseptic1488 [7]

Answer:

8. Domain: (-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)

9. Domain: [7/13, ∞)

Range: [1, ∞)

Step-by-step explanation:

Question 8

Given rational function:

$f(x)=\dfrac{x}{x^2+20x+75}$

Factor the denominator of the given rational function:

$\implies x^2+20x+75$

$\implies x^2+5x+15x+75$

$\implies x(x+5)+15(x+5)$

$\implies (x+15)(x+5)$

Therefore:

$f(x)=\dfrac{x}{(x+15)(x+5)}$

Asymptote: a line that the curve gets infinitely close to, but never touches.

The function is undefined when the denominator equals zero:

$x+15=0 \implies x=-15$

$x+5=0 \implies x=-5$

Therefore, there are vertical asymptotes at x = -15 and x = -5.

Domain: set of all possible input values (x-values)

Therefore, the domain of the given rational function is:

(-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)

---------------------------------------------------------------------------------

Question 9

Given function:

$f(x)=\sqrt{13x-7}+1$

Domain: set of all possible input values (x-values)

As the square root of a negative number is undefined:

$\implies 13x-7\geq 0$

$\implies 13x\geq 7$

$\implies x\geq \dfrac{7}{13}$

Therefore, the domain of the given function is:

$\left[\dfrac{7}{13},\infty\right)$

Range: set of all possible output values (y-values)

$\textsf{As }\:\sqrt{13x-7}\geq 0$

$\implies \sqrt{13x-7}+1\geq 1$

Therefore, the range of the given function is:

[1, ∞)

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