7.4A & 7.7A Linear Relationships Knowledge 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?

Back

The slope of a line represents the rate of change between the two variables. 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 point where the line crosses the y-axis. It is the value of y when x is 0.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

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

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as one variable increases, the other variable decreases, showing an inverse relationship.

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.

Front

How can you determine if a relationship is linear from a table of values?

Back

If the differences between the y-values are constant for equal differences in the x-values, the relationship is linear.

Front

What is the rate of change in a linear function?

Back

The rate of change is the same as the slope of the line, representing how much y changes for a unit change in x.

Front

What is the equation of a line that passes through the points (1, 2) and (3, 6)?

Back

First, find the slope: m = (6 - 2) / (3 - 1) = 2. Then use point-slope form: y - 2 = 2(x - 1), which simplifies to y = 2x.