Flashcard Review 8.2.5: Writing Linear Equations

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

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

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

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 y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

Write the equation of a line with a slope of 2 and a y-intercept of -3.

Back

y = 2x - 3.

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 the x-coordinate of any point on the line.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = b, where b is the y-coordinate of any point on the line.

Front

How do you convert the equation 2x + 3y = 6 to slope-intercept form?

Back

Rearranging gives y = -2/3x + 2.

Front

What is the significance of the coefficients in the equation y = mx + b?

Back

m is the slope, indicating the steepness, and b is the y-intercept, indicating where the line crosses the y-axis.

Front

If a line has a slope of 0, what type of line is it?

Back

A line with a slope of 0 is a horizontal line.