Finding 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/run).

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept of a linear equation is the point where the line crosses the y-axis. It can be found by setting x = 0 in the equation and solving for y.

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 y-intercept represent in a graph?

Back

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

Front

If a line has a slope of 2, what does this indicate about the line's steepness?

Back

A slope of 2 indicates that for every 1 unit increase in x, the value of y increases by 2 units, making the line relatively steep.

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is 0, indicating that there is no change in y as x changes.

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined, as it would involve division by zero (change in x is 0).

Front

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

Back

The slope can be determined using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line from left to right.

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.