Old Ch. 3 - Slope/Slope-intercept Form

Front

What is the definition of slope in a linear equation?

Back

Slope is a measure of the steepness of a line, represented as the ratio of the vertical change to the horizontal change between two points on the line.

Front

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

Back

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

Front

How do you determine if a slope is undefined?

Back

A slope is undefined when the line is vertical, meaning there is no horizontal change (the denominator of the slope formula is zero).

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates that the line is horizontal, meaning there is no vertical change as you move along the line.

Front

How can 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 y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

If a line has a slope of 4, what does this mean in terms of rise over run?

Back

A slope of 4 means that for every 1 unit you move horizontally (run), the line rises 4 units vertically (rise).

Front

What is the equation of a line with a slope of -5/3 and a y-intercept of 1?

Back

The equation of the line is y = -5/3x + 1.

Front

How do you convert the slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms involving x and y on one side.

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 relationship where one quantity changes in relation to another.