Suppose you have a sample of n points for two variables: (x1, y1), (x2, y2), ... (xn, yn). Without going into various statistical considerations (which are nonetheless important) you can estimate the slope of the 'best' line that can be used to estimate the values of y from the values of x using for formula given for beta-hat in the wikipedia article for simple linear regression.
Standard. You need a linear equation in two variables for slope-intercept form.
line graph
The slope between two parallel lines is identical. This is because parallel lines have the same slope and will never intersect. The slope of a line is a measure of its steepness, and when two lines are parallel, they will have the same steepness, resulting in the same slope. Therefore, the slope between two parallel lines will always be equal.
For a direct variation equation the constant MUST be 0. Then the ratio of a pair of values of the two variables is the slope.
slope intercept form, rise over run
The slope of a line is the same thing as the rate of change between two variables in a linear relationship.
A line graph is used to compare two specific variables.
If the two variables are directly proportional, then the slope can be any number,but the y-intercept has to be zero ... the line must go through the origin.
A graph of two simultaneous linear inequalities in two variables that have no intersecting regions must contain two lines with the same slope.
Negative
The slope of a line on a graph represents the rate of change between two variables. A steeper slope indicates a faster rate of change, while a shallower slope indicates a slower rate of change. The slope can provide information about the relationship between the variables being compared.
two different variables
The slope of a line represents the rate of change between two variables. A positive slope indicates a direct relationship, where one variable increases as the other increases. A negative slope indicates an inverse relationship, where one variable decreases as the other increases. The steeper the slope, the greater the rate of change between the variables.
Standard. You need a linear equation in two variables for slope-intercept form.
line graph
For a direct variation equation the constant MUST be 0. Then the ratio of a pair of values of the two variables is the slope.
slope intercept form, rise over run