Verified Answer :

calculista

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

\(y=-\frac{5}{3}x\)


raphealnwobi

The equation of  the line that passes through the origin is y = -5x / 3

Linear equation

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept

The slope of the line AB passing through A(-3, 0) and B(-6, 5) is given by:

AB = (5 - 0)/ (-6 - (-3)) = -5/3

Two lines are parallel if they have the same slope. Since the line passes through (0, 0), hence:

y - 0 = (-5/3)(x - 0)

y = -5x / 3

The equation of  the line that passes through the origin is y = -5x / 3

Find out more on Linear equation at: https://brainly.com/question/14323743

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