Solving Systems by Graphing

Front

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

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

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

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, indicating how steep the line is.

Front

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

Back

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

Front

How can you find the solution to a system of equations graphically?

Back

The solution to a system of equations can be found by graphing both equations and identifying the point(s) where they intersect.

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the solution to the system, indicating the values of x and y that satisfy both equations.

Front

What is a consistent system of equations?

Back

A consistent system of equations has at least one solution, meaning the lines intersect at one or more points.

Front

What is an inconsistent system of equations?

Back

An inconsistent system of equations has no solutions, meaning the lines are parallel and never intersect.

Front

What is the solution to the system of equations 2x + 3y = 6 and x - y = 1?

Back

The solution to the system is (3, 0).

Front

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

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).