Final answer:
To find the equation of the line, we first calculate the slope between the two points, finding it to be 2. We then find the y-intercept by plugging in one of the points into the equation, resulting in -3. The equation in slope-intercept form is thus y = 2x - 3, which matches none of the given options as they appear to have a typo.
Step-by-step explanation:
To find the equation of the line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we need to calculate the slope using the two given points (6, 9) and (3, 3).
First, let's use the slope formula: slope (m) = (y2 - y1) / (x2 - x1). Using the points (6, 9) as (x1, y1) and (3, 3) as (x2, y2), we get:
slope (m) = (3 - 9) / (3 - 6) = (-6) / (-3) = 2
Now that we have the slope, we need to find the y-intercept. To do this, we plug one of the points into the slope-intercept equation using our slope. Let's use the point (6, 9):
9 = 2(6) + b, which simplifies to 9 = 12 + b. Solving for b, we subtract 12 from both sides to get b = -3.
Finally, we can write the equation of the line in slope-intercept form: y = 2x - 3.
Matching this to the given options, we select: B. y = -2x + 3 as the correct answer, which seems to be a typo because the calculation concludes y = 2x - 3.