Writing Linear Equations

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm'. It is calculated as the change in y divided by the change in x (rise over run).

Front

How do you calculate 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 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 'b' in the slope-intercept form.

Front

What is a vertical line and how is it represented?

Back

A vertical line has an undefined slope and is represented by the equation x = a, where 'a' is the x-coordinate of any point on the line.

Front

What is an x-intercept?

Back

The x-intercept is the point where the line crosses the x-axis, represented as (x, 0).

Front

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

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What is the formula for writing the equation of a line given a point and the slope?

Back

The equation can be written using point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the difference between positive and negative slopes?

Back

A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right.

Front

How do you convert from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y.