Slope and Y-intercept

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically 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 y-intercept of a linear equation?

Back

The y-intercept of a linear equation is the point where the line crosses the y-axis. It can be found by setting x = 0 in the equation and solving for y.

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

If the slope of a line is negative, what does that indicate about the line's direction?

Back

A negative slope indicates that the line descends from left to right.

Front

What is the slope of the line represented by the equation y = -5x + 1?

Back

The slope of the line is -5.

Front

How can you determine the slope from two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the y-intercept of the equation y = 3/2x + 3?

Back

The y-intercept is the point (0, 3).

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, and use the slope to find another point. Draw a line through these points.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal.

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 any other ratio of change between two variables.