AB (with an arrow over AB I can't past the arrow so yeah) 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? (with an arrow over it again)
a)5x – 3y = 0
b)-x + 3y = 0
c)-5x – 3y = 0
d)3x + 5y = 0
e) -3x + 5y = 0
I meant paste the arrow!!
Does anyone know the answer???
the slope of AB is -5/3
so, which if the choices has that same slope?
To find the equation of the line that passes through the origin and is parallel to AB, we can follow these steps:
1. Find the slope of line AB: The slope formula between two points (x1, y1) and (x2, y2) is given by: slope = (y2 - y1) / (x2 - x1). In this case, A(-3, 0) and B(-6, 5).
Slope of AB = (5 - 0) / (-6 - (-3)) = 5 / (-3) = -5/3.
2. The line parallel to AB will have the same slope because parallel lines have equal slopes.
3. Since the line passes through the origin (0, 0), we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is any point on the line, and m is the slope.
4. Plugging in the values, we get: y - 0 = (-5/3)(x - 0)
Simplifying the equation, we have y = (-5/3)x.
Comparing this equation to the given answer choices, we can see that the correct equation is:
e) -3x + 5y = 0.