Question

Explain why it does not matter which point you choose when writing the equation of the line in point-slope form, given two points.

Which of the following is the most accurate explanation?

a) Point-slope form subtracts the X and y-values, so the slope of the line will always be positive.
b) A line that goes through both points has a constant slope, so choosing either point will result in an equivalent equation.
c) The point-slope form is based on two known points, so it will always produce the equation for a line, though different points will produce the equations for different lines.
d) Points on a line are always listed from left to right, so choosing the first point on the left will always ensure the same point is chosen for the second point.

Please choose the correct option.

Answer 1

It doesn't matter which point you choose when writing the equation in point-slope form because a line has a constant slope between any two points. Therefore, any point would lead to an equivalent equation with the same slope and y-intercept representation.

Step-by-step explanation:

The reason why it does not matter which point you choose when writing the equation of a line in point-slope form is that a line has a constant slope between any two points on it. Hence, choosing either point A or point B to write the point-slope form of the equation will result in an equivalent equation. This is because the slope of the line, calculated as the change in the vertical axis divided by the change in the horizontal axis, will be the same regardless of which point is chosen.

The y-intercept is the point where the line crosses the y-axis, and the slope is the measure of how steep a line is, which could be positive, negative, zero (for horizontal lines), or undefined (for vertical lines). The point-slope form of a line equation is represented as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Both points lie on the same straight line; thus, their slope with respect to any other point on the line, such as the y-intercept, is identical.