A line has slope -5/3 through two points could this line pass
Through the origin (0,0)?
To determine if a line with a slope of -5/3 passes through the origin, we need to see if the coordinates of the origin satisfy the equation of the line.
The equation of a line can be written in point-slope form as:
y - y₁ = m(x - x₁)
Where (x₁, y₁) are the coordinates of a point on the line and m is the slope.
Let's assume the two points are (x₁, y₁) and (x₂, y₂).
Using the given slope of -5/3, we can choose two convenient points. Let's say (0,0) and (3,5). This gives us:
(x₁, y₁) = (0,0)
(x₂, y₂) = (3,5)
Substituting these values in the equation, we get:
y - 0 = (-5/3)(x - 0)
y = (-5/3)(x)
y = (-5/3)x
Now, let's substitute the coordinates of the origin (0,0) into the equation:
0 = (-5/3)(0)
0 = 0
The equation holds true.
Therefore, a line with a slope of -5/3 passes through the origin (0,0).