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olga nikolaevna [1]
3 years ago
12

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

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<h2>hope it helps.</h2><h2>stay safe healthy and happy...</h2>
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Help me on this please
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At a bagel shop the first 6 bagels purchased cost 55 cents apiece, and additional bagels cost c cents apiece. If a customer paid
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Steve is turning half his backyard into a chicken fan. His backyard is a 24 m x 45 m rectangle. He wants to put a chicken wire f
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Step-by-step explanation:

Steve is turning half his backyard into a chicken fan. His backyard is a 24 m x 45 m rectangle. He wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. How many meters of fencing will Steve need?

We are to find the meters of fencing for the diagonal.

We solve the question using Pythagoras Theorem

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Hence:

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Distance of P from origin :

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