All categories

3 years ago

What is the equation of the following line? Be sure to scroll down first to see all answer options.

Mathematics

2 answers:

Masja [62]3 years ago

7 0

The equation of the following line is D. y = -6x

<h3>Further explanation</h3>

Let the linear equation : $y = mx + c$

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

<em>m → gradient of the line</em>

<em>( 0 , c ) → y - intercept</em>

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

$\large {\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}$

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

$\large {\boxed{y - y_1 = m ( x - x_1 )} }$

Let us tackle the problem.

From the attached picture, we can see a straight line through two points , (0,0) and (-½ , 3).

Let :

( 0 , 0 ) → ( x₁ , y₁ )

( -½ , 3 ) → ( x₂ , y₂ )

We can find the equation of solid line passing through points (x₁,y₁) and (x₂,y₂) by using this formula :

$\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}$

$\frac{y - 0}{3 - 0} = \frac{x - 0}{-\frac{1}{2} - 0}$

$\frac{y}{3} = \frac{x}{-\frac{1}{2}}$

$\frac{y}{3} = -2x$

$y = 3 \times (-2x)$

$\large {\boxed {y = -6x}}$

<h3>Learn more</h3>

Infinite Number of Solutions : brainly.com/question/5450548
System of Equations : brainly.com/question/1995493
System of Linear equations : brainly.com/question/3291576

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Equation , Line , Variable , Line , Gradient , Point

Harrizon [31]3 years ago

6 0

<h3><u>Answer:</u></h3>

Hence, the equation of line is:

y= -6x

<h3><u>Step-by-step explanation:</u></h3>

Clearly from the graph we could see that the line passes through the point (0,0) and (-1/2,3).

Also we know that the equation of a line passing through (a,b) and (c,d) is given as:

$y-b=\dfrac{d-b}{c-a}\times (x-a)$

Here we have:

(a,b)=(0,0) and (c,d)=(-1/2,3)

Hence, the equation of line is:

$y-0=\dfrac{3-0}{-\dfrac{1}{2}-0}\times (x-0)\\\\\\\\y=\dfrac{3}{\dfrac{-1}{2}}\times x\\\\y=3\times (-2)\times x\\\\y=-6x$

Hence, the equation of line is:

y= -6x

You might be interested in

I need help in this!

In-s [12.5K]

For a function to begin to qualify as differentiable, it would need to be continuous, and to that end you would require that $a$ is such that

$\displaystyle\lim_{x\to0^-}g(x)=\lim_{x\to0^+}g(x)\iff\lim_{x\to0}ax=\lim_{x\to0}x^2-3x$

Obviously, both limits are 0, so $g$ is indeed continuous at $x=0$ .

Now, for $g$ to be differentiable everywhere, its derivative $g'$ must be continuous over its domain. So take the derivative, noting that we can't really say anything about the endpoints of the given intervals:

$g'(x)=\begin{cases}a&\text{for }x0\end{cases}$

and at this time, we don't know what's going on at $x=0$ , so we omit that case. We want $g'$ to be continuous, so we require that

$\displaystyle\lim_{x\to0^-}g'(x)=\lim_{x\to0^+}g'(x)\iff\lim_{x\to0}a=\lim_{x\to0}2x-3$

from which it follows that $a=-3$ .

3 0

3 years ago

Given angle measurements of 40°, 45°, and 95°, how many triangles can be constructed?

natta225 [31]

I think the answer is (c)

5 0

3 years ago

Read 2 more answers

Use the equation to complete an algebraic proof that proves the answer is x = 7/6. Write your proof in your journal and upload y

dimaraw [331]

Answer:

Step-by-step explanation:

Show that if 3x – 7 = 5, then x = 4.

Here, our given statement is 3x – 7 = 5, and we're asked to prove x = 4.

x=4

Statements Reasons

1. 3x – 7 = 5 Given

2. 3x – 7 + 7 = 5 + 7 Addition of 7 to equation (1)

3. 3x + 0 = 5 + 7 Substitution of –7 + 7 = 0 into (2)

4. 3x = 5 + 7 Substitution of 3x + 0 = 3x into (3)

5. 3x = 12 Substitution of 5 + 7 = 12 into (4)

6. 3x⁄3 = 12⁄3 Dividing equation (5) by 3

7. x = 12⁄3 Substitution of 3x⁄3 = x into (6)

8. x = 4 Substitution of 12⁄3 = 4 into (7)

Is there such a thing as being too descriptive? Yep, and that was it, since over half the proof was devoted to telling the reader how to do arithmetic. We'll typically take numerical computation for granted, and write proofs like this:

5 0

3 years ago

Given the following: P(A) =0.3 P(B) = 0.2 P(A OR B) = 0.5 P(A AND B) = 0 Which of the following is true?a. A and B are disjoint.

erastova [34]

Answer:

a. A and B are disjoint

Step-by-step explanation:

We know that P(A and B)=0, It means that event A and event B have nothing in common and it means that event A and event B are disjoints events.

The event A and event B are independent if

P( A and B)= P(A)*P(B)

P(A)*P(B)=0.3*0.2=0.06

So, P(A and B)≠P(A)*P(B)

Hence events A and B are not independent.

Option a is A and B are disjoints which is correct

Option b is A and B are neither disjoints nor independent which is partially false as A and B are disjoints event.

Option c states that A and B are independent which is clearly false.

Option d states that A and B are disjoints and independent which is partially false as A and B are not independent.

Hence the correct option is option A.

5 0

3 years ago

Write as many equations as possible that could represent the relationship between

IgorC [24]

Answer:

a) Here we have:

"In Family A, the youngest child is 7 years younger than the oldest, who is 18"

Let's define:

Y = age of the youngest child.

O = age of the oldest child.

Then we know that:

Y = O - 7

O = 18

Then we can replace the second equation into the first one:

Y = 18 - 7 = 11.

b) Here we have:

"In Family B, the middle child is 5 years older than the youngest child."

Let's define:

Y = age of the youngest child.

M = age of the middle child.

Here we have only one equation:

M = Y + 5.

5 0

3 years ago