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4 years ago

Determine the equations of the straight lines

Mathematics

1 answer:

Ostrovityanka [42]4 years ago

3 0

Answer:

1). 6x - 14 2). y = 1x + 1 3). y = -4x + 22 4).y = -7/2x + 51/2

Step-by-step explanation:

1). y2 - y1 / x2 - x1 4 - (-2) / 3-2 = 6

y = 6x + b 4 = 6(3) + b 4 = 18 + b -14 = b

y = 6x - 14

2). 2 - (-2) / 1 - (-3) = 1

y = 1x + b 2 = 1(1) + b 2 = 1 + b 1 = b

y = 1x + 1

3). 2 - 6 / 5 - 4 = -4

y = -4x + b 6 = -4(4) + b 6 = -16 + b 22 = b

y = -4x + 22

4). 1 - 8 / 7 - 5 = -7/2

y = -7/2x + 51/2

You might be interested in

Which equation represents the magnitude of an

Basile [38]

Answer:

$M=\log{(100S)}$

Step-by-step explanation:

The <em>Richter scale</em>, the standard measure of earthquake intensity, is a <em>logarithmic scale</em>, specifically logarithmic <em>base 10</em>. This means that every time you go up 1 on the Richter scale, you get an earthquake that's 10 times as powerful (a 2.0 is 10x stronger than a 1.0, a 3.0 is 10x stronger than a 2.0, etc.).

How do we compare two earthquake's intensities then? As a measure of raw intensity, let's call a "standard earthquake" S. What's the magnitude of this earthquake? The magnitude is whatever <em>power of 10</em> S corresponds to; to write this relationship as an equation, we can say $10^m=S$ , which we can rewrite in logarithmic form as $m=\log{S}$ .

We're looking for the magnitude M of an earthquake 100 times larger than S, so reflect this, we can simply replace S with 100S, giving us the equation

$M=\log{(100S)}$ .

To check to see if this equation is right, let's say we have an earthquake measuring a 3.0 on the Richter scale, so $3=\log{S}$ . Since taking 100 times some intensity is the same as taking 10 times that intensity twice, we'd expect that more intense earthquake to be a 5.0. We can expand the equation $M=\log{(100S)}$ using the product rule for logarithms to get the equation

$M=\log{(100S)}=\log{100}+\log{S}$

And using the fact that $\log{100}=2$ and our assumption that $\log{S}=3$ , we see that $M=2+3=5$ as we wanted.

3 0

4 years ago

Which of the following is an equation for a line that is NOT parallel to the other three?

galben [10]

The equation of the line that is not parallel to others is (C) 2x-3y= -1

<h3>How to determine the equation of the line is not parallel?</h3>

From the question, we have the following parameters that can be used in our computation:

A) 3x-2y=5

B) -3x+2y=9

C) 2x-3y= -1

D) -3x+2y=8

Make y the subject in equations

So, we have the following representation

A) y = 3/2x - 5/2

B) y = 3/2x + 9/2

C) y= 2/3x + 1/3

D) y = 3/2x + 4

As a general rule of linear equations

Parallel lines have equal slope

A linear equation is represented as

y = mx + c

Where

slope = m

Using the above as a guide, we have the following:

A) y = 3/2x - 5/2 ⇒ slope = 3/2

B) y = 3/2x + 9/2 ⇒ slope = 3/2

C) y= 2/3x + 1/3 ⇒ slope = 2/3

D) y = 3/2x + 4 ⇒ slope = 3/2

Hence, the line that is not parallel is (c)