Slope Review / Word Problems

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 vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate 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 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 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

What is the significance of the y-intercept in a linear equation?

Back

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

Front

How can you determine the rate of change from a linear equation?

Back

The rate of change is represented by the slope of the line in the equation, indicating how much y changes for a unit change in x.

Front

What does the equation 4x - 8y = 16 represent in slope-intercept form?

Back

To convert to slope-intercept form, solve for y: y = (1/2)x - 2.

Front

How do you identify the graph of a horizontal line?

Back

A horizontal line has a slope of 0 and is represented by the equation y = b, where b is a constant.

Front

How do you identify the graph of a vertical line?

Back

A vertical line has an undefined slope and is represented by the equation x = a, where a is a constant.

Front

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

Back

The slope of the line is -1.