Equation of a straight line part two

We can examine the second defining property of y = 2x + 1 by looking at the same table below.

x-101234
y-113579

As the value of x increases by 1, the value of y increases by 2. When x is 0, y is 1. When x increases to 1, y is 3 and when x increases to 2, y is 5. We can see that y increases by 2 when x increases by 1. This is called the step-size. The step-size of the equation of the straight line y = 2x + 1 is 2.

Let’s find the step-size of other equations of a straight line.

y = 5x + 2

x0123
y271217

As x increases from 0 to 1 to 2, y increases from 2 by 5 to 7 and then to 12. The step-size of y = 5x + 2 is 5.

Let’s look at one more.

y = -7x + 2

x0123
y2-5-12-19

As x increases from 0 to 1 to 2, y decreases from 2 to -5 to -12. The step-size of y = -7x + 2 is -7.

The step-size is the number that comes in front of the x in an equation of a straight line.

Let’s look at a table of the step-size for some equations of a straight line.

EquationValue of the step-size
y = 5x + 25
y = 5x + 35
y = -7x + 2-7
y = -7x - 7-7
y = 10x + 9910