THE COMPONENTS OF A LINEAR EQUATION

Mr. Huynh

The Linear Equation

A linear equation can contain many parts such as this one: y = 2 x + 6. What does this all mean? To break it down, we must look at the initial form which is:

y = m x + b

What does each variable represent?

Each variable in y = m x + b represents a specific value.

y = dependent variablem = slope (or change from one point to

another)x = independent variableb = y-intercept

X and Y relationship

The x and y variables have a relationship. Y is the dependent variable because its value varies on x, hence x is the independent variable.

Example: y = 2x + 6If x = 2 y = 2(2) + 6 y = 10If x = 4 y = 2(4) + 6 y = 14The value of y depends on what the given x

will be.

Slope

Definition: The ratio from vertical change to horizontal change between two points on a line. It measures the steepness.

Slope can be calculated by using two points and plugging it into the following formula:

m (slope) = (1st y value – 2nd y value)/(1st x value – 2nd x value)

Slope Example

Take points (-3, 0) and (0 , 6). Simply plug it into your equation and you will obtain your slope.

m (slope) = (1st y value – 2nd y value)/(1st x value – 2nd x value)

m = (0 – 6)/(-3 – 0) = -6/-3 = 2

Y – Intercept

The final value that is noted in y = mx + b is b. B denotes the y-intercept or the point where the line hits the y-axis on the graph. Going back to our previous example, y = 2x + 6, our y-intercept is 6.

Example of the intercept is in the next slide.

Y-Intercept = 6