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2 years ago

How do I find the function rule??? x: 0, 1, 2, 3 y: 5, 4, 3, 2

Mathematics

1 answer:

Makovka662 [10]2 years ago

8 0

Answer: y=-1x+5

Step-by-step explanation:

1. Use slope-intercept formula (y = mx + b) to find the slope which is represented by the variable 'b'.

m = ∆y / ∆x

m = -1 / 1

m = -1

y= -1x + b

2. Use any cooresponding x and y values to substitute into the formula. Ex: (x,y) → (1,4)

y = mx + b

4 = -1(1) + b

4 = -1 + b

5 = b

3. Plug in the values found into the formula.

y = -1x + 5

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

What are the roots to<br> the equation<br> 2x² + 6x-1=0?

lys-0071 [83]

Answer:

The roots of equations are as m = $\frac{-3}{2} + \frac{\sqrt{11} }{2}$ And n = $\frac{-3}{2} - \frac{\sqrt{11} }{2}$

Step-by-step explanation:

The given quadratic equation is 2 x² + 6 x - 1 = 0

This equation is in form of a x² + b x + c = 0

Let the roots of the equation are ( m , n )

Now , sum of roots = $\frac{ - b}{a}$

And products of roots = $\frac{c}{a}$

So, m + n = $\frac{ - 6}{2}$ = - 3

And m × n = $\frac{ - 1}{2}$

Or, (m - n)² = (m + n)² - 4mn

Or, (m - n)² = (-3)² - 4 ( $\frac{ - 1}{2}$ )

Or, (m - n)² = 9 + 2 = 11

I.e m - n = $\sqrt{11}$

Again m + n = - 3 And m - n = $\sqrt{11}$

Solving this two equation

(m + n) + ( m - n) = - 3 + $\sqrt{11}$

I.e 2 m = - 3 + $\sqrt{11}$

Or, m = $\frac{-3}{2} + \frac{\sqrt{11} }{2}$

Similarly n = $\frac{-3}{2} - \frac{\sqrt{11} }{2}$

Hence the roots of equations are as m = $\frac{-3}{2} + \frac{\sqrt{11} }{2}$ And n = $\frac{-3}{2} - \frac{\sqrt{11} }{2}$ Answer

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