A line passes through the points (8, –1) and (–4, 2). What is the y-intercept of this line?

1 answer:

4 0

Y=mx+b
m=slope
b=y intercept

alrighty, find the slope

slope between (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)

the slope between (8,-1) and (-4,2) is (2-(-1))/(-4-8)=(2+1)/(-12)=3/-12=-1/4

y=(-1/4)x+b
find b
subsitute a point
(8,-1)
x=8 and y=-1
-1=(-1/4)(8)+b
-1=-2+b
1=b

the y intercept is y=1 or the point (0,1)

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General Formulas and Concepts:

Pre-Algebra

Equality Properties

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Calculus

Derivatives

Basic Power Rule:

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Step-by-step explanation:

Step 1: Define

$ln(\frac{2x-1}{x-1} )=t$

Step 2: Differentiate

Rewrite: $t = ln(\frac{2x-1}{x-1})$
Rewrite [Ln Properties]: $t = ln(2x-1) - ln(x - 1)$
Differentiate [Ln/Chain Rule/Basic Power Rule]: $\frac{dt}{dx} = \frac{1}{2x-1} \cdot 2 - \frac{1}{x-1} \cdot 1$
Simplify: $\frac{dt}{dx} = \frac{2}{2x-1} - \frac{1}{x-1}$
Rewrite: $\frac{dt}{dx} = \frac{2(x-1)}{(2x-1)(x-1)} - \frac{2x-1}{(2x-1)(x-1)}$
Combine: $\frac{dt}{dx} = \frac{-1}{(2x-1)(x-1)}$
Reciprocate: $\frac{dx}{dt} = -(2x-1)(x-1)$
Distribute: $\frac{dx}{dt} = (1-2x)(x-1)$