(2) The graph of a linear function passes through the points \( (3,19) \) and \( (5,23) \). Write an equation for the function. Show your work.

To find the equation of the linear function that passes through the points \( (3,19) \) and \( (5,23) \), we can start by calculating the slope \( m \). The formula for slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting in our points, we have: \[ m = \frac{23 - 19}{5 - 3} = \frac{4}{2} = 2 \] Now that we have the slope, we can use the point-slope form of the equation, which is: \[ y - y_1 = m(x - x_1) \] Using point \( (3, 19) \): \[ y - 19 = 2(x - 3) \] Now, simplifying this: \[ y - 19 = 2x - 6 \\ y = 2x + 13 \] Thus, the equation of the function is: \[ y = 2x + 13 \] Now you can plot this line, and it will beautifully intersect your given points!