Unit 5 & 6 Flashcard

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you find the slope from the equation x + 2y = 8?

Back

To find the slope, rearrange the equation into slope-intercept form (y = mx + b). For x + 2y = 8, subtract x from both sides: 2y = -x + 8, then divide by 2: y = -1/2x + 4. The slope (m) is -1/2.

Front

What is the slope of the line represented by the equation y = -4x + 5?

Back

The slope of the line is -4, as it is the coefficient of x in the slope-intercept form (y = mx + b).

Front

What does the equation y = 7.5x represent in a real-world context?

Back

This equation represents a linear relationship where for every hour worked (x), Carlo earns $7.50 (y).

Front

How can you express the number of unopened bottles of water Joe has after x days?

Back

The number of unopened bottles can be expressed as 24 - 2x, where 24 is the initial number of bottles and 2x represents the bottles consumed after x days.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the rate of change between the two variables represented in the equation. A positive slope means an increase, while a negative slope indicates a decrease.

Front

How do you interpret a slope of -3 in a graph?

Back

A slope of -3 means that for every 1 unit increase in x, y decreases by 3 units, indicating a steep downward trend.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero in the slope formula.