WU 3.2B: Identifying Slope and Y-Intercept

Front

What is the definition of the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise over run).

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 the value of y when x is 0, typically represented as 'b' in the equation of a line (y = mx + b).

Front

How do you find the slope from a linear equation in slope-intercept form?

Back

In slope-intercept form (y = mx + b), the slope 'm' is the coefficient of x.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no change in y regardless of the change in x.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x is 0, leading to division by zero.

Front

How can you determine the y-intercept from a linear equation in standard form?

Back

To find the y-intercept from standard form (Ax + By = C), set x = 0 and solve for y.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3, as it is the coefficient of x in the equation.

Front

If a line has a slope of -2, what does this indicate about its direction?

Back

A slope of -2 indicates that the line descends from left to right, meaning for every 1 unit increase in x, y decreases by 2 units.

Front

What is the y-intercept of the equation y = -4x + 5?

Back

The y-intercept is 5, as it is the value of y when x = 0.

Front

How do you convert the equation y = 2x + 1 to standard form?

Back

To convert to standard form (Ax + By = C), rearrange to get -2x + y = 1 or 2x - y = -1.