Writing Linear Equations from a Graph

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 is the value of y when x = 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 standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can 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 x into the equation and see if the resulting y value matches the y-coordinate of the point.

Front

What is the significance of the graph of a linear equation?

Back

The graph of a linear equation visually represents the relationship between x and y, showing all possible solutions to the equation.

Front

How do you write the equation of a line given the slope and y-intercept?

Back

Use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.