we know that
if two lines are parallel, then their slope are the same
[tex]m1=m2[/tex]
Step 1
Find the slope of the given line AB
the slope of the line is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]A(-3,0)\ B(-6,5)[/tex]
substitute the values
[tex]m=\frac{5-0}{-6+3}[/tex]
[tex]m=\frac{5}{-3}[/tex]
[tex]m=-\frac{5}{3}[/tex]
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 [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this case the constant of proportionality is equal to the slope
[tex]k=-\frac{5}{3}[/tex]
The equation is equal to
[tex]y=-\frac{5}{3}x[/tex]
therefore
the answer is
[tex]y=-\frac{5}{3}x[/tex]
The equation of the line that passes through the origin is y = -5x / 3
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
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