How do you find the equation of a linear relationship from a graph?

Answer 1

y=mx+b means that m is the slope, x is the variable, and b is the y intercept.

[ADDED] The gradient m is given by the difference formula [ y2 - y1) / (x2 - x1) ] where the 1 and 2 signify separate ordinates and the y-values are those from their corresponding x-values.

NB: they are not powers or factors here, but the text editor's limits makes typing algebra difficult.

In words, it is the change in the y-value given by a chosen change in the x-value.

So if the equation is y = 3x, lets take the values of x as 1 and 4. Therefore, the slope = [ (12-3) / (4-1) ]

= 9/3 = 3.

Important: always take the 1 and 2 co-ordinates in that rising-x order, not necessarily smaller-from-larger in y, because if the graph slopes down to the right the y-difference will be a negative number so the gradient is negative, and that is its correct description.

AS AN ASIDE because we need not complicate things by invoking calculus for simple linear graphs, that difference-over-difference formula in calculus notation is shown by the operator, dy/dx; and the process is called "differentiation". Worth recalling when you proceed to studying Calculus, which analyses non-linear equations!