Final answer:
The equation representing a line passing through the point (3, 5) with a y-intercept of -1 is y = 2x + 1. This is found by calculating the slope between the given point and the y-intercept and applying the point-slope form equation.
Step-by-step explanation:
The linear equation representing a line that passes through the point (3, 5) and has a y-intercept of -1 can be found using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Since we have a point and the y-intercept, the slope can be calculated as the change in y divided by the change in x between the given point and the y-intercept. Here, the slope m is (5 - (-1))/(3 - 0) = 6/3 = 2. Therefore, using the point-slope form with our point (3, 5), and slope 2, the equation is y - 5 = 2(x - 3). Simplifying this, we get y = 2x + 1, which is the equation of the desired line.