Find the equation of the line passing through the points (12, 9) and (10,15). Does this line pass through the origin?

A simple method to find the equation of a line is y - y₁ = m (x -x₁). First, find the gradient. m = (15-9)/ (10-12), which can be simplified to 6/-2. This gives the gradient a value of -3. We now have the equation y - y₁ = -3 (x -x₁). By feeding any of the coordinates given in the question (12, 9) into this formula, we have y - 9= -3 (x - 12). To eliminate the brackets, multiply through by -3, to give y - 9 = -3x + 36. To put this in the form required, move the -9 over to the other side of the equal to sign, now producing y = -3x + 36 + 9. When simplified, we have the equation of the line, which is y = -3x + 45. To answer the second part of the question, insert the coordinates (0, 0) into the equation of the line. This gives us 0 = -3(0) +45. When simplified, we get 0 = 45, which is incorrect, proving that the line does not pass through the origin.