Final answer:
The slope of the line through the points (5,18) and (10,3) is -3. A calculation error occurred with the y-intercept, which should be 33 and does not match the given options. The correct slope-intercept form based on these points is y = -3x + 33.
Step-by-step explanation:
To find the slope and y-intercept of the line passing through two points, you can use the slope formula and the concept of the slope-intercept form of a line, which is y = mx + b. First, we calculate the slope (m) by taking the difference in y-coordinates and dividing by the difference in x-coordinates: m = (y2 - y1) / (x2 - x1). For the points (5,18) and (10,3), the slope is (3 - 18) / (10 - 5) = -15 / 5, which simplifies to -3.
Next, we use one of the points and the slope to solve for the y-intercept (b). Let's use the point (5, 18):
18 = (-3)(5) + b. Simplifying, we get 18 = -15 + b, so b = 18 + 15, which results in a y-intercept of 33. However, this y-intercept does not match any of the options given. If we take another look at the question, we might realize there has been a mistake in transcription; as none of the listed options for y-intercept are correct. The correct slope and y-intercept based on our calculation are -3 and 33, respectively.
Since the error lies in the y-intercept, we must reassess our calculations or the question's given options. Although, based on our correct method, it appears Option C has the right slope but an incorrect y-intercept. The correct slope-intercept form based on the calculated values would be y = -3x + 33.