Review of Slope and Y-intercept

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 '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/run).

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 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 does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by 'b' in the slope-intercept form.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates that the line is horizontal.

Front

If a line has an undefined slope, what does that indicate about the line?

Back

An undefined slope indicates that the line is vertical.

Front

How can you determine the slope from the equation of a line in standard form (Ax + By = C)?

Back

To find the slope from standard form, rearrange the equation into slope-intercept form (y = mx + b) and identify 'm'.

Front

What is the slope of the line represented by the equation 2x + 3y = 6?

Back

First, rearrange to slope-intercept form: 3y = -2x + 6, then y = -2/3x + 2. The slope (m) is -2/3.

Front

What is the slope of a line that rises 4 units for every 2 units it runs?

Back

The slope is calculated as rise/run = 4/2 = 2.

Front

How do you interpret a negative slope?

Back

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