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2 years ago

Complete the slope-intercept form of the linear equation that represents the relationship in the table.

Mathematics

1 answer:

nevsk [136]2 years ago

6 0

According to the given table, the slope-intercept equation of the line is given by:

$y = -2x + 1$

The equation of a line, in <em>slope-intercept</em> form, is given by:

$y = mx + b$

In which:

The slope is m.

The intercept is b.

In this problem, we are given two points, (3,-5) and (-2,5).

The slope is given by <u>change in y divided by change in x</u>, hence:

$m = \frac{5 - (-5)}{-2 - 3} = -2$

Hence:

$y = -2x + b$

Point (3,-5) means that when $x = 3, y = -5$ , which is used to find b.

$y = -2x + b$

$-5 = -2(3) + b$

$b = 1$

Hence, the equation of the line is:

$y = -2x + 1$

A similar problem is given at brainly.com/question/24685547

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Analyze the key features of the graph f(x) = 1/x+3 -2

tia_tia [17]

<h2>Explanation:</h2><h2></h2>

Here we have the following rational function:

$f(x) = \frac{1}{x+3} -2$

So the graph of this function is shown in the First Figure below. Let's define another function which is a parent function:

$g(x)=\frac{1}{x}$

Whose graph is shown in the second figure below. So we can get the graph of f from the graph of g this way:

Step 1. Shift the graph 3 units to the left:

$f_{1}(x) = \frac{1}{x+3}$

Step 2. Shift the graph 2 units down:

$f(x) = \frac{1}{x+3}-2$

Finally, the features of the graph of f are:

The graph of this function comes from the parent function g and the transformations are:

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A shifting 2 units down

8 0

3 years ago

1. Show work and find the value of the circumference of the circle with a 12 cm radius.

Virty [35]

Answer:

75.36

Step-by-step explanation:

3.14(pi) x 24(diameter) = 75.36(circumference)

5 0

3 years ago

How can you write 1,360/200 as a repeating decimal?

Alisiya [41]

1360/200

13.6/2

6.8

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3 years ago

Solve: In 2x + In 2 = 0<br> DONE

pychu [463]

Answer:

$x=\frac{1}{4}$

Step-by-step explanation:

We can use some logarithmic rules to solve this easily.

<em>Note: Ln means $Log_e$ </em>

<em />

Now, lets start with the equation:

$ln(2x) + ln(2) = 0\\ln(2x) = -ln(2)$

Writing left side with logarithmic base e, we have:

$Log_{e}(2x) = -ln(2)$

We can now use the property shown below to make this into exponential form:

$Log_{a}b=x\\means\\a^x=b$

So, we write:

$Log_{e}(2x) = -ln(2)\\e^{-ln(2)}=2x$

We recognize another property of exponentials:

$a^{bc}=(a^{b})^{c}$

So, we write:

$e^{-ln(2)}=2x\\(e^{ln(2)})^{-1}=2x$

Also, another property of natural logarithms is:

$e^{(ln(a))}=a$

Now, we simplify:

$(e^{ln(2)})^{-1}=2x\\(2)^{-1}=2x\\\frac{1}{2}=2x\\x=\frac{\frac{1}{2}}{2}\\x=\frac{1}{4}$

This is the answer.

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3 years ago

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inessss [21]

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Step-by-step explanation:

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3 years ago