Solving Systems of Equations by Graphing

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the rise over run, or the change in y divided by the change in x.

Front

How do you find the slope from two points on a graph?

Back

To find the slope (m) from two points (x1, y1) and (x2, y2), use the formula: m = (y2 - y1) / (x2 - x1).

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 but different y-intercepts, indicating that the system of equations has no solution.

Front

What is the graphical representation of a system of equations with one solution?

Back

A system of equations with one solution is represented graphically by two lines that intersect at a single point.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the point (or points) where the graphs of the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

What does it indicate if a system of equations has infinitely many solutions?

Back

If a system of equations has infinitely many solutions, it means the equations represent the same line, and every point on that line is a solution.

Front

How can you determine if a system of equations has no solution?

Back

A system of equations has no solution if the lines are parallel, meaning they never intersect.

Front

What is the y-intercept in the equation of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as 'b' in the equation y = mx + b.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the slope and y-intercept, plot the y-intercept on the graph, and use the slope to find another point, then draw a line through the points.

Front

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

Back

The point of intersection represents the solution to the system, where all equations are satisfied simultaneously.