Flashcard Review - Point-Slope, Slope Intercept, Standard

Front

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

Back

The point-slope form is given by the equation y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is 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 given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the standard form of a linear equation?

Back

The standard form is given by Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

Convert the point-slope equation y - 7 = ⅔(x + 4) to slope-intercept form.

Back

y = ⅔x + 11/3.

Front

What does the term 'y-intercept' mean?

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 identify the slope from the equation y = -2x + 5?

Back

The slope is -2, which is the coefficient of x in the slope-intercept form.

Front

What is the significance of the coordinates (x1, y1) in the point-slope form?

Back

They represent a specific point on the line used to define the line's equation.

Front

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

Back

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