Answer:
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Using the given points (-3, 6) and (-3, 9), we can see that x1 = x2 = -3, and y1 = 6, y2 = 9. Substituting these values into the slope formula gives:
m = (9 - 6) / (-3 - (-3)) = 3/0
Note that the denominator of the fraction is zero, which means that the slope is undefined. This is because the two given points have the same x-coordinate, which means that they lie on a vertical line.
To find the y-intercept of the line, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is one of the given points. We can choose either (-3, 6) or (-3, 9) as our point, since they both lie on the line. For example, using (-3, 6) gives:
y - 6 = undefined(x - (-3))
Since the slope is undefined, we cannot use this equation to find the y-intercept. However, we can see from the given points that the line passes through the point (-3, 6). This means that the y-intercept is simply the y-coordinate of this point, which is:
b = 6
Therefore, the equation of the line passing through the points (-3, 6) and (-3, 9) is simply:
x = -3
Note that this is a vertical line passing through the point (-3, 6), and it has an undefined slope.