Graphing Linear Functions

Front

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

Back

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

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 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 the value of y when x = 0.

Front

How can 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, solve for y: y = (-A/B)x + (C/B).

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of y with respect to x; a positive slope means the line rises, while a negative slope means it falls.

Front

What is the slope of the line represented by the equation y = -3x + 7?

Back

The slope of the line is -3.

Front

How do you identify the y-intercept from the equation y = mx + b?

Back

The y-intercept is the value of b in the equation y = mx + b.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = a, where 'a' is a constant.

Front

How do you graph a linear equation using the slope and y-intercept?

Back

Start at the y-intercept on the y-axis, then use the slope (rise/run) to find another point on the line.