Question

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

Answer 1

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

Further explanation

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

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

m → gradient of the line

( 0 , c ) → y - intercept

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 :

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

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

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

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

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

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

Learn more

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

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

Answer 2

Answer:

Hence, the equation of line is:

y= -6x

Step-by-step explanation:

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