Linear Relationships Multiple Representations

Front

What is a linear relationship?

Back

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

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you write the equation of a line given a slope and a point?

Back

You can use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). In contrast, a relation can have multiple outputs for a single input.

Front

How can you represent a linear relationship using a table?

Back

A linear relationship can be represented using a table of values where each row corresponds to an (x, y) pair that satisfies the linear equation.

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What is the equation for a line with a slope of 2 and a y-intercept of -3?

Back

The equation is y = 2x - 3.

Front

How do you determine the total cost from a linear equation?

Back

To determine the total cost from a linear equation, substitute the value of the independent variable (e.g., number of items) into the equation to find the corresponding total cost.

Front

What does it mean if a linear equation has a negative slope?

Back

If a linear equation has a negative slope, it means that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.