Final answer:
The linear function rule for the line passing through points (5, 18) and (8, 21) is y = x + 13, which is found by calculating the slope and the y-intercept using the points given.The correct option among those provided is a)
Step-by-step explanation:
To find the linear function rule for a line passing through two particular points, you need to determine the slope (m) and the y-intercept (b) of the equation in the slope-intercept form (y = mx + b)
First, you calculate the slope using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. For points (5, 18) and (8, 21), the slope m is (21 - 18) / (8 - 5) = 3 / 3 = 1.
Next, you use the slope and one of the points to solve for the y-intercept b using the equation y = mx + b.
Plugging in one point, for example, (5, 18), with m = 1, we get 18 = 1(5) + b, which simplifies to b = 13. Thus, the equation of the line is y = x + 13.
Therefore, the correct option among those provided is a) y = x + 13.