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 (m) represent in a linear equation?

Back

The slope (m) 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 does the y-intercept (b) represent 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 determine the equation of a line from a graph?

Back

To determine the equation of a line from a graph, identify the slope (rise over run) and the y-intercept. Use the slope-intercept form y = mx + b to write the equation.

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 can you find the slope between 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 difference between a positive slope and a negative slope?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant. A negative slope indicates that as x increases, y decreases, resulting in a downward slant.

Front

What does it mean if a line is horizontal?

Back

A horizontal line has a slope of 0, meaning that the y-value remains constant regardless of the x-value. Its equation is of the form y = b.

Front

What does it mean if a line is vertical?

Back

A vertical line has an undefined slope, meaning that the x-value remains constant regardless of the y-value. Its equation is of the form x = a.

Front

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

Back

First, calculate the slope using the two points. Then, use one of the points and the slope to write the equation in point-slope form: y - y1 = m(x - x1).