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 from 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 by the value of b in the slope-intercept form.

Front

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

Back

A slope of 0 indicates that the line is horizontal.

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

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.

Front

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

Back

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

Front

How do you convert the point-slope form to slope-intercept form?

Back

Rearrange the equation y - y1 = m(x - x1) to solve for y, resulting in y = mx + (y1 - mx1).

Front

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

Back

The slope indicates the steepness and direction of the line; a positive slope rises, while a negative slope falls.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.