instruction: If a straight line passes through the points (4,2) and (8,6) then where does it cross the x axis? Explain your answer.
response: First, you must calculate the gradient of the line by finding the change in y over the change in x. In this case, between the first point and the second point the y co-ordinate increases by 6-2=4 and the x co-ordinate increases by 8-4=4, so the gradient is 4/4=1. We are looking at a straight line with the equation y=x+c for some value of c, which we can find by plugging in one of our points, for example, 4=2+c, so c must be 2, and the equation of the line is y=x+2. When a line crosses the x axis then it's y co-ordinate is 0. Therefore in this case the line crosses the x axis at x=-2.