1. Find the equation of the line given the points (2, 3) and (5, 12) lie on this line.2. Explain how you checked that your answer was correct

To find the equation of the line, we first need to find the slope (m). The formula for the slope when given two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1).

Substituting the given points (2, 3) and (5, 12) into the formula, we get:

m = (12 - 3) / (5 - 2) = 9 / 3 = 3

Now that we have the slope, we can use the point-slope form of the line equation, which is y - y1 = m(x - x1).

Substituting m = 3 and the point (2, 3) into the equation, we get:

y - 3 = 3(x - 2)

Simplifying this equation gives us the equation of the line:

y = 3x - 3

To check if the equation is correct, we can substitute the given points into the equation and see if they satisfy it.

For the point (2, 3), substituting x = 2 into the equation gives us y = 3*2 - 3 = 3, which is correct.

For the point (5, 12), substituting x = 5 into the equation gives us y = 3*5 - 3 = 12, which is also correct.

Therefore, the equation y = 3x - 3 is indeed the equation of the line that passes through the points (2, 3) and (5, 12).