Slope, Intercepts, and Graphing Lines

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, represented as the ratio of the rise (change in y) to the run (change in x). It is often denoted as 'm' in the equation of a line, y = mx + b.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of 'b' in the equation y = mx + b.

Front

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

Back

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

Front

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

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the x-intercept of a line?

Back

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0.

Front

How do you find the x-intercept from the equation 9x - 6y = 36?

Back

To find the x-intercept, set y = 0 and solve for x: 9x = 36, so x = 4.

Front

What is the relationship between the slope and the direction of a line?

Back

A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right.

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates a horizontal line, which means 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, where x remains constant while y changes.

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and use the formula m = rise/run.