Question

Consider the formula for the slope between two coordinate points, m, shown below.

M=y₂-y₁/x₂-x₁

Which of the following equations is equivalent to the slope formula?

A.) Y₂=m(x₂-x₁)+y₁

B.) X₂=m(y₂-y₁)+x₁

C.) Y₁=m(x₂-x₁)+y₂

D.) X₁=m(y₂-y₁)+x₂

Answer 1

Option A (Y₂ = m(x₂ - x₁) + y₁) is the correct equation equivalent to the slope formula because it aligns with the line equation derived using the slope, whereas the other options do not match the slope-intercept form of a linear equation.

Step-by-step explanation:

The question asks which of the given equations is equivalent to the slope formula, given as m = (y₂ - y₁) / (x₂ - x₁). Considering this formula, we understand that slope (m) represents how much the y-value changes for a unit change in the x-value on a straight line. Now, if we were to write an equation of a line in terms of y, using the slope and known coordinates, we would get y - y₁ = m(x - x₁), which can be rewritten as y = m(x - x₁) + y₁ when we solve for y.

Comparing this to the given options, option A (Y₂ = m(x₂ - x₁) + y₁) aligns with the derived formulation of the line's equation using the slope. Hence, option A is the correct equivalent expression for the slope formula, where m represents the slope of the line, and (x₂ - x₁) represents the horizontal change between two points on the line.