graphing and substitution systems

Front

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

Back

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

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What is the graphical representation of the equation y = -x + 2?

Back

It is a straight line with a slope of -1 and a y-intercept at (0, 2).

Front

What is the solution to the system of equations y = 2x - 11 and y = 2x + 5?

Back

The system has no solutions because the lines are parallel.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How do you determine the intersection point of two lines graphically?

Back

The intersection point is where the two lines cross each other on the graph.

Front

What is the solution to the system of equations 2x - y = 0 and 4x - y = 0?

Back

The solution is (0, 0) because both equations represent the same line.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

How can you tell if two lines are parallel from their equations?

Back

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