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3 years ago

Please find the slope and the equation.and step by step explanation PLEASE.

Mathematics

1 answer:

Lisa [10]3 years ago

3 0

Answers:

slope = 1
equation is y = x-4

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Explanation:

Two points on this diagonal line are (0,-4) and (1,-3)

Let's apply the slope formula to get the following

m = (y2-y1)/(x2-x1)

m = (-3-(-4))/(1-0)

m = (-3+4)/(1-0)

m = 1/1

m = 1

The slope is 1. We can think of it as 1/1 to indicate "go up 1, and over to the right 1". In other words, slope = rise/run = 1/1.

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Note how the graph crosses the y axis at -4, so this is the y intercept.

Since the y intercept is -4, this means b = -4

So with m = 1 and b = -4, we go from y = mx+b to y = 1x+(-4) which simplifies to y = x-4

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3 years ago

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Answer:

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3 years ago

The derivative (4x+1)^2

Jobisdone [24]

Answer:

$\displaystyle \frac{d}{dx}[(4x + 1)^2] = 8(4x + 1)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = (4x + 1)^2$

Step 2: Differentiate

Basic Power Rule [Derivative Rule - Chain Rule]: $\displaystyle y' = 2(4x + 1) \cdot \frac{d}{dx}[4x + 1]$
Basic Power Rule [Addition/Subtraction, Multiplied Constant]: $\displaystyle y' = 2(4x + 1) \cdot 4$
Simplify: $\displaystyle y' = 8(4x + 1)$