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
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