Linear Relationships Review

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 represents 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

Write the equation of a line with a slope of 1 and a y-intercept of 2.

Back

y = 1x + 2 or y = x + 2.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

If a line has a slope of -3, what does this indicate about the relationship between x and y?

Back

A slope of -3 indicates that for every 1 unit increase in x, y decreases by 3 units, showing an inverse relationship.

Front

What does it mean if two lines are parallel?

Back

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

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, indicating they intersect at a right angle.

Front

How can you determine the cost of snowboarding for x hours if the resort charges $15 per hour and $25 for board rental?

Back

The cost can be represented by the equation y = 15x + 25, where y is the total cost and x is the number of hours.