why do we change the signs of x and y values in point slope form
In point-slope form, the equation of a line is written as:
y - y₁ = m(x - x₁),
where (x₁, y₁) is a point on the line and m is the slope of the line.
The reason for changing the signs of the x and y values in point-slope form is to represent the relationship between the point (x₁, y₁) and any other point (x, y) on the line.
When you subtract x₁ from x (x - x₁), you are calculating the horizontal distance between the two points on the x-axis. By subtracting y₁ from y (y - y₁), you are calculating the vertical distance between the two points on the y-axis.
So, changing the signs of x and y values allows you to determine the change in x and y coordinates from the reference point (x₁, y₁) to any other point on the line.