Linear Equations

Welcome to Linear Equations! Your one-stop-shop for basic Linear Algebra. Linear equations make life very easy! You can predict (see into) the future outcomes of certain problems.

The most common linear equation (rule or function) is y = mx + b.

To actually use this equation, you have to know what the variables represent, and what they mean. So let's break it down.

M is the constant rate of change (slope) which is known as m = Δ y ÷ Δ x = vertical change/horizontal change = rise/run In the case of our table, the x value increases by 1, while the y value by 5, so we divide the change in y by the change in x. In the example of our table, this is 3 ÷ 1 = 3.

B is the y-intercept (starting value or flat fee). B can be found by looking for the y value when the x value is 0, either by backtracking on your table or seeing the corresponding number to the x value equaling 0. That's the y-intercept; in the table below, it's 5.

Firstly, plug in the formula. For example: if I want to find what the y value will be, when the x value is 279, I plug in 279 for x: y = 3(279) + 5. Once solved, you should get an answer of 842.
But, what if you want to find the x value when the y value is 842? Well that's actually quite simple, you can find the x value by plugging in 842 for y: 842 = 3x + 5. Now all you have to do is inverse operations, and once solved you should get an answer of 279!

↻ Flip Table
x 0 1 2 3 4 5
y 5 8 11 14 17 20