Final answer:
To find the equation of a line passing through two points, use the point-slope formula. The slope is found using the formula (y2 - y1) / (x2 - x1). Substitute the slope and the coordinates of one point into the point-slope formula to find the equation of the line.
Step-by-step explanation:
To find the equation of a line passing through two points, we can use the point-slope formula: y - y1 = m(x - x1). First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). For the first set of points (1, 4) and (6, 14), the slope is: m = (14 - 4) / (6 - 1) = 10/5 = 2. Second, we can choose either point and substitute its coordinates into the point-slope formula, along with the slope, to find the equation of the line. Let's use the point (1, 4): y - 4 = 2(x - 1). Simplifying gives us: y - 4 = 2x - 2. Rearranging the equation gives us the final equation of the line: y = 2x + 2. Let's follow the same steps for the second set of points (1, -2) and (6, 23).