solving systems by graphing

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never intersect. They have the same slope.

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

How do you find the slope of a line from two points?

Back

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

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form.

Front

How do you graph a line using the slope-intercept form?

Back

1. Plot the y-intercept (0, b). 2. Use the slope (rise/run) to find another point. 3. Draw the line through the points.

Front

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

Back

A system of equations has no solution if the lines are parallel and never intersect.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the point where the two lines intersect.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the two equations represent the same line.

Front

What is the first step in graphing a line?

Back

The first step is to plot the y-intercept on the graph.