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3 years ago

Work out the equation of the line which has a gradient of 2 and passes through the point (1, 4)

Mathematics

1 answer:

leva [86]3 years ago

4 0

Answer:

y = 2x + 2

Step-by-step explanation:

The slope is also called the gradient of the line.

The slope that is given is two, and the point is (1, 4).

I made a point slope equation, and then converted it into a slope-intercept equation.

$y-4=2(x-1)\\\\y-4=2x-2\\\\y-4+4=2x-2+4\\\\\boxed{y=2x+2}$

Hope this helps.

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Line 1: 2x-3y>12

nata0808 [166]

Answer:

The graph of this line i.e. $2x-3y>12$ should be BELOW the DOTTED line as $y$ involves < symbol.
The graph of this line i.e. $y>-2x+5$ should be ABOVE the DOTTED line as it involves > symbol.
The correct graph for line 1 and line 2 is shown in attached figure.

Step-by-step explanation:

If the inequality involves < or >, then the graph of the equation involves a dotted line.
If the inequality involves ≤ or ≥, then the graph of the equation involves a solid line.

Considering the line 1

$2x-3y>12$

Solving line 1

$2x-3y>12$

$-3y>12-2x$

$3y$

$y$

As $y$ involves < symbol, so the graph of this line should be BELOW the DOTTED line.

But, as you can see that there is an error in the graph. As the graph of $y$ is being shown ABOVE the SOLID line.

Therefore, the graph of this line i.e. $y$ should be BELOW the DOTTED line as it involves < symbol.

Considering the line 2

$y>-2x+5$

As $y>-2x+5$ involves > symbol, so the graph of this line should be ABOVE the DOTTED line.

But, as you can see that there is an error in the graph. As the graph of $y>-2x+5$ is being shown ABOVE the SOLID line.

Therefore, the graph of this line i.e. $y>-2x+5$ should be ABOVE the DOTTED line as it involves > symbol.

The correct graph for line 1 i.e. $2x-3y>12$ and line 2 i.e. $y>-2x+5$ is shown in attached figure.

From the attached graph, it is shown that only (5, -2) satisfies the both inequalities. So, (5, -2) is the correct solution for the given inequalities.

Solution Verification:

Putting (5, -2) in line 1 and line 2

For line 1:

2x - 3y > 12 ⇒ 2(5) - 3(-2) > 12 ⇒ 10 + 6 > 12 ⇒ 16 > 12 which is true.

For line 2:

y > -2x + 5 ⇒ -2 > -2(5) + 5 ⇒ -2 > -10 + 5 ⇒ -2 > -5 which is true.

So, (5, -2) is IN the solution for line 1 and line 2

Putting (-1, -1) in line 1 and line 2

For line 1:

2x - 3y > 12 ⇒ 2(-1) - 3(-1) > 12 ⇒ -2 + 3 > 12 ⇒ 1 > 12 which is false.

For line 2:

y > -2x + 5 ⇒ -1 > -2(-1) + 5 ⇒ -1 > 2 + 5 ⇒ -1 > 7 which is false.

So, (-1, -1) is NOT in the solution for line 1 and line 2

Putting (0, 5) in line 1 and line 2

For line 1:

2x - 3y > 12 ⇒ 2(0) - 3(5) > 12 ⇒ 0 - 15 > 12 ⇒ -15 > 12 which is false.

For line 2:

y > -2x + 5 ⇒ 5 > -2(0) + 5 ⇒ 5 > 0 + 5 ⇒ 5 > 5 which is false.

So, (0, 5) is NOT in the solution for line 1 and line 2

Keywords: inequality, solution, graph, dotted line, solid line

Learn more about inequality solution from brainly.com/question/12036085

#learnwithBrainly

4 0

4 years ago

Is 98 a perfect square?

UNO [17]

No

..................………

7 0

4 years ago

Read 2 more answers

X^2=1 has two solutions. If the equation is changed to 4x^2=1 which operation find the solutions of the new equation?

snow_lady [41]

Answer:

X = -1/2 or 1/2

Step-by-step explanation:

When the square root of a number is found, this usually results in 2 solutions which may be equal in size but opposite in signs.

As such,

X^2=1 to find x find the root of both sides

X = √1

X = -1 or 1

Going by this

4x^2=1

Divide both sides by 4

X^2=1 /4

taking the square root of both sides

X = √1/4

The root of 1 is -1 or 1 while that of 4 is -2 or 2 hence,

X = -1/2 or 1/2

3 0

3 years ago

The frequency f of vibration of a violin string is inversely proportional to its length L. The constant of proportionality k is

Natali5045456 [20]

Answer:

(A) $f=\frac{k}{L}$

(B) Frequency becomes half.

Step-by-step explanation:

We have been given that the frequency f of vibration of a violin string is inversely proportional to its length L. The constant of proportionality k is positive and depends on the tension and density of the string.

(A) We know that two inversely proportional quantities are in form $y=\frac{k}{x}$ , where y is inversely proportional to x and k is constant of proportionality.

Upon substituting our given values, we will get:

$f=\frac{k}{L}$

Therefore, our required equation would be $f=\frac{k}{L}$ .

(B) For part, we have been given that length is twice, so our new frequency will be $f_n$ and new length $L_n$ is $2L$ .

Upon substituting $2L$ in our equation as:

$f_n=\frac{k}{L_n}$

$f_n=\frac{k}{2L}$

$f_n=\frac{1}{2}\cdot \frac{k}{L}$

$f_n=\frac{1}{2}\cdot f$

Upon comparing $f_n$ with $f$ , we can see that $f_n$ is half the value of $f$ .

Therefore, the frequency of vibration of violin gets half, when we double the length of the string.

3 0

3 years ago

What is the area of this triangle in the coordinate plane?

Klio2033 [76]

Hey. Let me help you on this one.

In order for us to solve this problem, we will be needing to find both length and width of the triangle on this coordinate plane. We will also need to know how to use the triangle area formula.

I will be attaching an image containing the shown difference between a rectangle, and a triangle, and on how to understand why the area of a triangle is like this.

First of all, let's find the length of the triangle. It's 11 units, and we can determine that by counting up all of the units, or simply finding the difference between x-point 13 and 2, which is going to be 11.

Same applies to the width of the triangle. We will need to either count up all the units individually, or find a difference between a higher y-point and lower y-point. That difference is going to 5 units, since $9-4=5$ .

Now, let's use the formula for the triangle area and substitute the values.

$S= \frac{a*b}{2}$
$S= \frac{11*5}{2}$
$S= \frac{55}{2}$
$S=27.5$

Answer: Area of the triangle on the coordinate plane is 27.5 units squared.

3 0

4 years ago

Read 2 more answers