Algebra I - Chapter 5 Review

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line, and is calculated as the change in y divided by the change in x (rise over run).

Front

How do you determine if the slope of a line is positive, negative, or zero?

Back

A positive slope means the line rises from left to right, a negative slope means it falls from left to right, and a slope of zero indicates a horizontal line.

Front

What is the formula to calculate 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 the y-intercept of a line represent?

Back

The y-intercept is the point where the line crosses the y-axis, represented as 'b' in the slope-intercept form of a line, y = mx + b.

Front

How can you find the y-intercept from the equation of a line?

Back

To find the y-intercept, set x = 0 in the equation of the line and solve for y.

Front

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

Back

The slope of the line y = 3 is 0, as it is a horizontal line.

Front

What is the slope of the line represented by the equation y = -rac{1}{2}x - 5?

Back

The slope of the line is -rac{1}{2}.

Front

If a line has a slope of 2, what does this indicate about the line's steepness?

Back

A slope of 2 indicates that for every 1 unit increase in x, y increases by 2 units, making the line relatively steep.

Front

What is the significance of a negative slope in a real-world context?

Back

A negative slope can indicate a decrease in value, such as a decline in temperature or a decrease in sales over time.

Front

How do you graph a line given its slope and y-intercept?

Back

Start at the y-intercept on the y-axis, then use the slope to determine the rise over run to plot additional points.