Question

Which of the following represent(s) an equation of the line passing through the points A(5,6) and B(4,8). Select all that apply.

a. \(y = -2x + 16\)

b. \(y = 2x - 4\)

c. \(y = -2x + 6\)

d. \(y = 2x + 4\)

Answer 1

The equation of the line passing through the points A(5,6) and B(4,8) is y = -2x + 16.

Step-by-step explanation:

To find the equation of the line passing through the points A(5,6) and B(4,8), we can use the point-slope formula, which states that the equation of a line passing through a point (x1, y1) with slope m is given by y - y1 = m(x - x1). Plugging in the values from point A, we have y - 6 = m(x - 5). Now, we can substitute the values from point B and solve for m. Doing so, we get 8 - 6 = m(4 - 5), which simplifies to m = -2. Plugging this value of m back into the equation, we get y - 6 = -2(x - 5), which can be rearranged to y = -2x + 16. This shows that option A, y = -2x + 16, represents the equation of the line passing through the given points.

So, the correct answer is: a. y = -2x + 16.