slope and y-intercept from a table

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 change in the y-coordinate to the change in the x-coordinate (rise over run).

Front

How do you calculate the slope from a table of values?

Back

To calculate the slope from a table, select two points (x1, y1) and (x2, y2) and use the formula: slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line descends from left to right.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How can you find the y-intercept from a table of values?

Back

To find the y-intercept from a table, look for the value of y when x is 0.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope of the line is 2, which indicates that for every unit increase in x, y increases by 2 units.

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal, indicating that the y-value remains constant regardless of the x-value.

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you interpret a slope of -4?

Back

A slope of -4 means that for every 1 unit increase in x, y decreases by 4 units.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates in various contexts.