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3 years ago

What is the equation of a line that has a y-intercept of 4 and an x-intercept of -2?

Mathematics

1 answer:

Furkat [3]3 years ago

6 0

Answer:

y = 2x + 4

Step-by-step explanation:

Two points on this line are (-2, 0) and (0, 4). Going from the first to the second, x increases by 2 (this is the 'run') and y increases by 4 ('rise').

Thus, the slope of this line is m = rise / run = 4/2 = 2

Using the slope-intercept formula, we get y = mx + b = 2x + b

Let x = -2 and y = 0 to find b: 0 = 2(-2) + b, so b = 4, and the desired equation is then:

y = 2x + 4

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3 years ago

write the logarithm as a sum or difference of logarithms. simplify each term as much as possible. log4(6ab)

Dominik [7]

The logarithm written as a sum of logarithm and simplified as much as possible is $\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

<h3>Simplifying Logarithms</h3>

From the question, we are to write the given logarithm expression as a sum or difference of logarithms

The given logarithm is

$log_{4 }6ab$

This can be written as

$log_{4 }6 \times a \times b$

From one of the rules of logarithm, we have that

$log_{x }yz= log_{x }y + log_{x }z$

Thus,

$log_{4 }6 \times a \times b$ becomes

$log_{4 }6 + log_{4 }a + log_{4 }b$

This can be further simplified into

$log_{4 }3 \times 2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + log_{4 }2 + log_{4 }a + log_{4 }b$

If desired, this can be further simplified into

$log_{4 }3 + log_{2^{2} }2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + \frac{1}{2} log_{2}2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + \frac{1}{2} (1)+ log_{4 }a + log_{4 }b$

$\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

Hence, the logarithm written as a sum of logarithm and simplified as much as possible is $\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

Learn more on Simplifying logarithms here: brainly.com/question/17851187

#SPJ1

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2 years ago

What is the equation of a line that has a y-intercept of 4 and an x-intercept of -2?​

What is the equation of a line that has a y-intercept of 4 and an x-intercept of -2?