Writing Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope goes up, negative slope goes down).

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

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

Back

The slope (m) can be 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 of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you convert a linear equation 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 to isolate it on one side of the equation.

Front

What does it mean if the slope of a line is zero?

Back

If the slope of a line is zero, it means the line is horizontal and there is no change in y as x changes.

Front

What does it mean if the slope of a line is undefined?

Back

If the slope of a line is undefined, it means the line is vertical and there is no change in x as y changes.

Front

How do you determine if a point (x, y) lies on the line represented by a linear equation?

Back

To determine if a point (x, y) lies on the line, substitute the x-value into the equation and see if the resulting y-value matches the y-value of the point.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope but different y-intercepts.