Solving Systems by Graphing Review

Front

What is the y-intercept of a line?

Back

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

Front

How do you determine the number of solutions in a system of equations?

Back

The number of solutions can be determined by analyzing the graphs of the equations: one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line).

Front

What is the standard format for an ordered pair?

Back

An ordered pair is written in the format (x, y), where x is the value on the horizontal axis and y is the value on the vertical axis.

Front

How do you graph the equation y = -3x + 4?

Back

To graph y = -3x + 4, start at the y-intercept (0, 4) and use the slope of -3 to find another point by going down 3 units and right 1 unit.

Front

What does the solution to a system of equations represent graphically?

Back

The solution represents the point where the graphs of the equations intersect.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have the same slope and will never intersect, indicating that the system has no solution.

Front

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

Back

The slope-intercept form, y = mx + b, allows you to easily identify the slope (m) and the y-intercept (b) of the line.

Front

How can you find the x-intercept of a line?

Back

To find the x-intercept, set y to 0 in the equation and solve for x.

Front

What is the graphical representation of the equation y = 2x - 1?

Back

The graph of y = 2x - 1 is a straight line with a slope of 2 and a y-intercept of -1.