Functions Review

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 slope-intercept form of a linear equation (y = mx + b). It is calculated as the rise over run, or the change in y divided by the change in x.

Front

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

Back

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

Front

What does the variable 'b' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

How do you find the equation of a line given a slope and a y-intercept?

Back

To find the equation of a line given a slope (m) and a y-intercept (b), use the slope-intercept form: y = mx + b.

Front

What is the y-intercept of the line represented by the equation y = 2x + 5?

Back

The y-intercept of the line y = 2x + 5 is 5, which is the value of y when x = 0.

Front

If a line has a slope of 1/2, what does this indicate about the line?

Back

A slope of 1/2 indicates that for every 2 units the line moves horizontally (run), it moves up 1 unit vertically (rise). This means the line rises gently.

Front

What is the significance of a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes. The equation of such a line is of the form y = b, where b is a constant.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line descends from left to right, meaning as x increases, y decreases.

Front

How can you determine the slope from two points on a line?

Back

To determine the slope from two points (x1, y1) and (x2, y2), use the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the equation of a line with a slope of -3 and a y-intercept of 2?

Back

The equation of the line is y = -3x + 2.