Final answer:
The equation of the line passing through the points (3,8) and (5,14) is found by calculating the slope and y-intercept, resulting in the function f(x) = 3x - 1.
Step-by-step explanation:
To find an equation of the line passing through the points (3,8) and (5,14), we first need to determine the slope (m) of the line. The slope is calculated using the formula m = (Y2 - Y1) / (X2 - X1), where (X1, Y1) and (X2, Y2) are the coordinates of the two points. Substituting the given points into the slope formula, we get m = (14 - 8) / (5 - 3) = 6 / 2 = 3.
Next, we use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. We already know m = 3, so we just need to find b. We can use one of the points to solve for b. Substituting point (3,8) into the equation, we get 8 = 3(3) + b, which simplifies to 8 = 9 + b. Therefore, b = -1.
Using function notation, the equation of the line is f(x) = 3x - 1. This line passes through the points (3,8) and (5,14) with a slope of 3 and a y-intercept of -1.