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 steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0, represented by the 'b' in the equation y = mx + b.

Front

How can a linear relationship be represented in a table?

Back

A linear relationship can be represented in a table by listing pairs of values (x, y) that satisfy the linear equation. Each pair shows the corresponding output (y) for a given input (x).

Front

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

Back

The equation of the line is y = 2x + 3.

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1). Then use the point-slope form y - y1 = m(x - x1) to write the equation.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts. This means they will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means one line has a slope that is the negative reciprocal of the other.

Front

How can you represent a linear relationship using a graph?

Back

A linear relationship can be represented using a graph by plotting points that correspond to the (x, y) pairs from the linear equation and connecting them to form a straight line.

Front

What is the formula for calculating the slope between two points?

Back

The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1).