Writing Linear Equations

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

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 does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the significance of a slope of 0 in a linear equation?

Back

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

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, where x remains constant while y changes.

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope.

Front

How can you determine if two lines are perpendicular using their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

Given the points (2, 8) and (3, 12), what is the slope of the line?

Back

The slope is 4, calculated as (12 - 8) / (3 - 2).

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

How do you write the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.