Question

AB passes through A(-3, 0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to AB ?

Answer 1

we know that

if two lines are parallel, then their slope are the same

$m1=m2$

Step 1

Find the slope of the given line AB

the slope of the line is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$A(-3,0)\ B(-6,5)$

substitute the values

$m=\frac{5-0}{-6+3}$

$m=\frac{5}{-3}$

$m=-\frac{5}{3}$

Step 2

Find the equation of the line that passes through the origin and is parallel to AB

we know that

If the line passes through the origin represent a direct variation and it can be expressed in the form $y/x=k$ or $y=kx$

In this case the constant of proportionality is equal to the slope

$k=-\frac{5}{3}$

The equation is equal to

$y=-\frac{5}{3}x$

therefore

the answer is

$y=-\frac{5}{3}x$

Answer 2

Answer:

The required equation of line : 5x + 3y = 0

Step-by-step explanation:

Let the required line be CD

Given : AB passes through A(-3,0) and (-6,5)

Since, AB ║ CD ⇒ the slope of AB = Slope of CD

Therefore, finding slope(m) of AB :

$m=\frac{y_2-y_1}{x_2-x_1}\\\\\implies m = \frac{5-0}{-6+3}\\\\\implies m = \frac{-5}{3}$

Now, CD passes through origin (0,0)

And the equation of line passing through one point (p,q) is given by :

(y - q) = m × (x - p)

⇒ The required equation of CD :

$y - 0=\frac{-5}{3}\times (x-0)\\\\\bf\implies 5x+3y=0$

Hence, the required equation of line : 5x + 3y = 0