Graphing Slope-Intercept Form

Front

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

Back

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

Front

What does the y-intercept represent in a graph?

Back

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

Front

How do you identify the slope from the equation y = mx + b?

Back

The slope (m) indicates the steepness of the line and the direction it goes; a positive slope rises to the right, while a negative slope falls to the right.

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 does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, meaning x remains constant while y changes.

Front

How can you graph the equation y = 2x + 3?

Back

Start at the y-intercept (0, 3) and use the slope (2) to rise 2 units up and run 1 unit to the right to find another point.

Front

What is the slope of the line represented by the equation y = -4x + 1?

Back

The slope is -4, indicating the line falls steeply as it moves to the right.

Front

How do you convert the equation y = 3x - 5 into slope-intercept form?

Back

The equation is already in slope-intercept form, where the slope is 3 and the y-intercept is -5.

Front

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

Back

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

Front

How do you determine if a line is increasing or decreasing from its slope?

Back

If the slope is positive, the line is increasing; if the slope is negative, the line is decreasing.