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2 years ago

Pls help i will give u brianliest

Mathematics

1 answer:

Fynjy0 [20]2 years ago

7 0

Answer:

Slope = -3

y-intercept = (0,-4)

Equation: y = -3x-4

Step-by-step explanation:

We can take any two input-output pairs from the table to find the equation of given function.

Linear function is given by:

$y =mx+b$

Here m is the gradient of the functions which is defined as:

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

The input-output pairs are:

(x1,y1) = (-1,-1)

(x2,y2) = (0,-4)

First of all,

$m = \frac{-4-(-1)}{0-(-1)}\\= \frac{-4+1}{1} = -3$

Putting the value of slope in the equation

$y = -3x+b$

Putting (-1,-1) in the equation

$-1 = -3(-1)+b\\-1 = 3+b\\b = -1-3\\b = -4$

The equation will be:

$y = -3x-4$

Hence,

Slope = -3

y-intercept = (0,-4)

Equation: y = -3x-4

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2 years ago

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2 years ago

Need help simplifying this

diamong [38]

The simplified answer is $\frac{\left(12 x^{2}+7 x y-4 y z-3 x z+3 y^{2}\right)}{6 x^{2}+3 x z+2 x y+y z}$ .

<u>Step-by-step explanation:</u>

$$\frac{3 y+2 x}{z+2 x}-\frac{2 y-3 x}{3 x+y}-\frac{2 z(y+3 x)}{6 x^{2}+3 x z+2 x y+y z}$

To add or subtract denominators of the fraction must be same.

If it is not the same, we must take LCM of the denominators. and so we can add the fractions.

To make the denominator same multiply the 1st term $(\frac{3x+y}{3x+y})$ and 2nd term by $(\frac{z+2x}{z+2x})$

= $\frac{(3 y+2 x)(3 x+y)}{(z+2 x)(3 x+y)}-\frac{(2 y-3 x)(z+2 x)}{(3 x+y)(z+2 x)}-\frac{2 z(y+3 x)}{6 x^{2}+3 x z+2 x y+y z}$

LCM of the denominators is 6x²+ 3xz + 2xy +yz.

Multiply the factors in the numerator.

= $\frac{\left(6 x^{2}+3 y^{2}+11 x y\right)}{(z+2 x)(3 x+y)}-\frac{\left(2 y z+4 x y-3 x z-6 x^{2}\right)}{(3 x+y)(z+2 x)}-\frac{2 z y+6 x z}{6 x^{2}+3 x z+2 x y+y z}$

Now, the denominators are same, you can subtract it.

= $\frac{\left(6 x^{2}+6 x^{2}+11 x y-4 x y-2 y z-2 y z+3 x z-6 x z+3 y^{2}\right)}{6 x^{2}+3 x z+2 x y+y z}$

= $\frac{\left(12 x^{2}+7 x y-4 y z-3 x z+3 y^{2}\right)}{6 x^{2}+3 x z+2 x y+y z}$

Thus the simplified solution is $\frac{\left(12 x^{2}+7 x y-4 y z-3 x z+3 y^{2}\right)}{6 x^{2}+3 x z+2 x y+y z}$

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2 years ago