IM Grade 8 Unit 3 Review

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as the ratio of the vertical change to the horizontal change between two points on the line.

Front

How do you determine if two quantities have a proportional relationship?

Back

Two quantities have a proportional relationship if they maintain a constant ratio or rate, meaning that as one quantity increases or decreases, the other does so in a consistent manner.

Front

What does the equation y = mx + b represent?

Back

This is the slope-intercept form of a linear equation, where m is the slope and b is the y-intercept.

Front

What is the slope of the line represented by the equation y = -3?

Back

The slope is 0, indicating a horizontal line.

Front

How can you identify a proportional relationship from a graph?

Back

A proportional relationship will show a straight line that passes through the origin (0,0) on a graph.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

In the equation y = (1/2)x + 8, what does the (1/2) represent?

Back

The (1/2) represents the slope of the line, indicating that for every 1 unit increase in x, y increases by 0.5 units.

Front

What type of graph would represent a constant rate of change?

Back

A linear graph, which is a straight line, represents a constant rate of change.

Front

What is the relationship between the slope and the steepness of a line?

Back

A larger absolute value of the slope indicates a steeper line, while a smaller absolute value indicates a less steep line.

Front

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

Back

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