Final answer:
The equation of the line passing through the points (3,19) and (7,23) is y = x + 16.
Step-by-step explanation:
The equation of the line passing through the points (3,19) and (7,23) can be found using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. First, we find the slope by using the formula m = (y2 - y1)/(x2 - x1). Substituting the values of the points, we get m = (23-19)/(7-3) = 4/4 = 1. Now, let's use one of the points to find the y-intercept. We can take point (3,19) and substitute the values of x and y in the equation, which gives us 19 = 1(3) + b. Solving for b, we get b = 16. Therefore, the linear function rule is y = x + 16.