Question

The points (6,9) and (9,8) fall on a particular line. What is its equation in point-slope form?

Option 1: y= −(1/3)x+11
Option 2: y= (1/3)x−11
Option 3: y= −(1/3)x−11
Option 4: y= (1/3)x+11

Answer 1

The equation of a line in point-slope form passing through (6,9) and (9,8) is y= −(1/3)x+11, which is Option 1. Thus, the correct equation in point-slope form is Option 1: y= −(1/3)x+11.

Step-by-step explanation:

The student asked about the equation of a line in point-slope form that passes through the points (6,9) and (9,8). To find the equation, we first calculate the slope (m) by taking the difference in y-coordinates over the difference in x-coordinates: m = (y2 - y1) / (x2 - x1) = (8 - 9) / (9 - 6) = -1 / 3. Next, we use one of the points and the slope to write the point-slope equation. Let's use (6,9): y - 9 = -(1/3)(x - 6). Now, we need to rearrange it into the y=mx+b form to see which option it corresponds to:

y - 9 = -(1/3)x + 2

y = -(1/3)x + 11

Thus, the correct equation in point-slope form is Option 1: y= −(1/3)x+11.