solving systems by graphing

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

What does it mean if a system of equations has 0 solutions?

Back

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

Front

What does it mean if a system of equations has infinite solutions?

Back

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

Front

What are the steps for graphing a line?

Back

1. Plot the y-intercept. 2. Use the slope to find a second point. 3. Draw the line through the points.

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 is the y-intercept of the equation y = 4x + 2?

Back

The y-intercept is 2, which is the point where the line crosses the y-axis.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

If two lines intersect at one point, how many solutions does the system have?

Back

The system has exactly one solution, which is the point of intersection.

Front

What is the graphical representation of the equation -8x + 2y = 4?

Back

To graph it, convert to slope-intercept form: y = 4x + 2.

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x + 4?

Back

The solution is the point where the two lines intersect, which can be found by solving the equations simultaneously.