Final answer:
To find a line parallel to another line, calculate the slope of the given line and use that slope to construct the new line. The equation of the line parallel to the given line passing through the point (2, 4) is y = x + 2.
Step-by-step explanation:
To find a line parallel to another line, we need to find the slope of the given line and use that slope to construct the new line. The slope between two points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1).
First, calculate the slope of the given line using the points (-10, 1) and (5, 16). The slope is (16 - 1) / (5 - (-10)) = 15 / 15 = 1.
Next, use the slope of 1 and the point (2, 4) to construct the equation of the parallel line. The equation will be y = mx + b, where m is the slope and b is the y-intercept. Substitute the values of m and the point (2, 4) into the equation to find the y-intercept:
y = 1 * x + b
4 = 2 + b
b = 2.
Therefore, the equation of the line parallel to the given line passes through the point (2, 4) and is y = x + 2.