Final answer:
The equation of a line parallel to y = 2x + 3 that passes through the point (3,1) is y = 2x - 5.
Step-by-step explanation:
To find the equation of a line parallel to y = 2x + 3 that passes through the point (3,1), we need to understand two main concepts: the slope of a line and the y-intercept. First, parallel lines have the same slope. Since the given equation has a slope of 2, our new line will also have a slope of 2. The general form of a line's equation is y = mx + b, where m is the slope and b is the y-intercept. We already know the slope (m=2), so we just need to find b, the y-intercept.
To find b, we can use the coordinates of the given point (3,1). Plugging these values into the slope-intercept form gives us 1 = (2)(3) + b. Solving for b, we get 1 = 6 + b, which simplifies to b = -5. Therefore, the equation of our line is y = 2x - 5.