Calculating gradients

Rise = how far up Run = how far across The gradient of a straight line is an indication of how steep a straight line is. When we draw graphs the method we use to calculate the gradient is: Rise = how far up Run = how far across

Calculate the gradient of a horizontal line: The slope of a horizontal line is always zero

Calculate the gradient of a vertical line: The slope of a vertical line is undefined because we cannot divide by zero

Summary Negative slope Positive slope Zero slope Undefined slope

Example: Calculate the gradient joining (-1,-3) to (5, 2) run = 6 rise = 5 How could we calculate gradient without drawing the diagram?

How can we calculate the gradient joining (x1,y1) to (x2,y2)? run = x2-x1 (x2,y2) rise = y2-y1 (x1,y1)

So, to summarise: Use when drawing graphs Use when graphs are not needed

Calculate the gradients of the line joining (4,-7) to (-2,-1): (4, -7) (-2, -1) (x1,y1) (x2,y2)

(5, -3) (k, -1) (x1,y1) (x2,y2)