Linear Relationships Prep

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be expressed in the form of an equation, typically y = mx + b, where m is the slope and b is the y-intercept.

The constant of proportionality is the constant value (k) that relates two proportional quantities. In the equation y = kx, k represents the constant of proportionality.

To find the constant of proportionality, divide the total amount by the number of units. For example, if 14 gallons of gas cost $48.86, the constant of proportionality is $48.86 / 14 = $3.49 per gallon.

The slope of a linear equation represents the rate of change between the two variables. It indicates how much y changes for a unit change in x.

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

A nonproportional relationship is a relationship between two variables that does not have a constant ratio. It can be represented by a linear equation that includes a y-intercept other than zero.

The slope of the equation y = 3x + 4 is 3.

To extend a table of values for a linear relationship, use the equation of the line to calculate the corresponding y-values for new x-values.

When x = 12, y = 3(12) + 4 = 36 + 4 = 40.

The formula for calculating the slope (m) is m = (y2 - y1) / (x2 - x1).