solving systems by graphing

Front

What is the solution to the system of equations represented by the intersection of two lines?

Back

The solution is the point where the two lines intersect, representing the values of the variables that satisfy both equations.

Front

What does it mean if two lines are parallel when graphing?

Back

Parallel lines never intersect because they have the same slopes.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

If m=3 and b=6, what is the slope-intercept equation?

Back

y = 3x + 6

Front

What is the solution when two lines are graphed and they overlap?

Back

The solution is infinite solutions, as every point on the line is a solution.

Front

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

Back

A system has no solution if the lines are parallel and do not intersect.

Front

What does it mean if two lines intersect at a single point?

Back

It means there is one unique solution to the system of equations.

Front

What is the significance of the y-intercept in a linear equation?

Back

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

Front

How can 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 happens when you graph the same equation twice?

Back

You will have infinite solutions, as both lines are identical.