Final answer:
The equation of the line that passes through (5, 2) and (8, 8) is y = 2x - 8, which can be found by calculating the slope using the two points and then solving for the y-intercept with the slope-intercept form of a line equation.
Step-by-step explanation:
To find the equation of a line in slope-intercept form, which is y = mx + b, we first need to determine the slope (m) of the line that passes through two given points, (5, 2) and (8, 8). The slope is calculated by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, m = (8 - 2) / (8 - 5) = 6 / 3 = 2. Now that we have the slope, we can use either of the two points to solve for the y-intercept (b) using the slope-intercept equation. Let's use the point (5, 2): 2 = 2(5) + b, which simplifies to 2 = 10 + b, and therefore b = 2 - 10 = -8. The final equation of the line is therefore y = 2x - 8, which is not one of the provided options.