8th Grade Linear Functions

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities where one of the quantities is expressed as a quantity of one. For example, if you can buy 36 cookies for $4, the unit rate is 9 cookies per dollar.

Front

How do you calculate the constant rate of speed?

Back

To calculate the constant rate of speed, divide the total distance traveled by the total time taken. For example, if a car travels 390 miles in 6 hours and 520 miles in 8 hours, the total distance is 910 miles and the total time is 14 hours, resulting in a speed of 65 miles per hour.

Front

What is the formula for calculating the slope of a line?

Back

The slope (m) of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line is descending from left to right.

Front

What is the slope of a line that passes through the points (10, 1) and (5, 2)?

Back

The slope of the line that passes through the points (10, 1) and (5, 2) is -1/5.

Front

What does a slope of -2 represent in a linear function?

Back

A slope of -2 means that for every 1 unit increase in x, the value of y decreases by 2 units.

Front

How can you interpret the slope in a real-world context?

Back

In a real-world context, the slope represents the rate of change between two variables. For example, if $500 is earned for every 8 hours worked, the slope indicates the earnings per hour.

Front

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

Back

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

Front

How do you find the y-intercept from a linear equation in slope-intercept form?

Back

In slope-intercept form (y = mx + b), the y-intercept is represented by the value of b.

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, while a negative slope indicates that as x increases, y decreases.