Linear Relationships Quick Check

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 in a linear equation?

Back

The slope (m) 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 one-unit increase in x.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you identify the constant of proportionality in a linear relationship?

Back

The constant of proportionality is the coefficient of x in the equation y = kx, where k represents the constant. It shows how much y changes for each unit change in x.

Front

What is the equation of a line that passes through the origin?

Back

The equation of a line that passes through the origin is of the form y = kx, where k is the slope.

Front

How can you determine if a relationship is proportional?

Back

A relationship is proportional if it can be represented by a linear equation of the form y = kx, where k is a constant. The graph of a proportional relationship is a straight line that passes through the origin.

Front

What does it mean for a graph to represent a linear equation?

Back

A graph represents a linear equation if it forms a straight line. Each point on the line corresponds to a solution of the equation.

Front

What is the significance of the equation y = 2x?

Back

The equation y = 2x indicates a linear relationship where for every 1 unit increase in x, y increases by 2 units. The slope is 2 and the y-intercept is 0.

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 find the equation.

Front

What is the relationship between the coefficients in the equation y = mx + b?

Back

In the equation y = mx + b, m is the slope of the line, which indicates the steepness and direction, while b is the y-intercept, which indicates where the line crosses the y-axis.