Final answer:
To find the equation of a line parallel to a given line and passing through a given point, determine the slope of the given line. Substitute the coordinates of the point into the equation and solve for the y-intercept. The resulting equation will have the same slope as the given line and pass through the given point.
Step-by-step explanation:
To find the equation of a line that is parallel to the given line and passes through the given point, we need to determine the slope of the given line. In the equation y = 5x + 10, the slope is 5. Since the parallel line will have the same slope, its equation will also be y = 5x + b, where b is the y-intercept. To find the value of b, we substitute the x and y coordinates of the given point (2, 14) into the equation and solve for b.
14 = 5(2) + b
14 = 10 + b
b = 4
Therefore, the equation of the line parallel to y = 5x + 10 and passing through the point (2, 14) is y = 5x + 4.