Question

The points (– 9,6) and (– 10,2) fall on a particular line. What is its equation in point-slope form?

Option 1: y=2x+20
Option 2: y=2x−20
Option 3: y=−2x−20
Option 4: y=−2x+20

Answer 1

After calculating the slope of the line passing through the points (– 9,6) and (– 10,2), and using the point-slope form, it is clear that none of the provided options matches the correct point-slope form equation of the line.

Step-by-step explanation:

To find the equation of the line in point-slope form that passes through the points (– 9,6) and (– 10,2), first, we calculate the slope (m) by using the slope formula m = (y2 - y1) / (x2 - x1). Using the given points, the slope would be:

m = (2 - 6) / (– 10 + 9)

m = – 4 / – 1

m = 4

Now using one of the given points, for example point (– 9,6), and the slope, the point-slope form equation y - y1 = m(x - x1) becomes:

y - 6 = 4(x + 9)

This equation must match one of the options provided. Expanding the equation, we get:

y - 6 = 4x + 36

Adding 6 to both sides gives us:

y = 4x + 42

None of the options provided match this equation. Therefore, there should be a revision of either the question or the options given.