Question

a line that passes through points (1,-2) and (-3,5). explain one way of finding the slope of this line.

Answer 1

First of all, I think you mean the slope of a line, where a line is defined as the join of two points. And a better word for slope would be “gradient", as this is a more precise word, so I'm going to be using this from now on, and I suggest you do the same. The algebra letter we use for the gradient will be m.

The gradient is basically a value which represents how steep a line is from the horizontal. Think of walking up a hilly road. The more steep the climb, the higher the gradient. But how do you work out this value for a theoretical line plotted on a graph?

A line plotted on cartesian axes, x and y, has the relation: y= mx + c, where m is the gradient, and c is the point at which the line crosses the y axis, also called the y-intercept. Here is a diagram to describe the concept: