Final answer:
The slope of the line through the points (-6, -6) and (-3, 0) is 2. The y-intercept, found by substituting a point and the slope into the equation y = mx + b, is 6. Therefore, the correct answer is option B).
Step-by-step explanation:
To find the y-intercept and slope for the given points (-6, -6) and (-3, 0), we need to utilize the slope formula and the concept of the y-intercept from the graph of a line. The slope (m) is found by dividing the change in y by the change in x (rise over run).
The slope is calculated as:
m = (y2 - y1) / (x2 - x1) = (0 - (-6)) / (-3 - (-6)) = 6 / 3 = 2
Since the slope is positive, for every 1 unit we move to the right on the x-axis, we move 2 units up on the y-axis. Now, to find the y-intercept, we can use one of the points and the slope to plug into the equation of a straight line, y = mx + b, and solve for b.
Using point (-3, 0) and the slope 2:
- 0 = 2*(-3) + b
- b = 0 + 6
- b = 6
Therefore, the y-intercept is 6 and the slope is 2, which matches option B).