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

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 does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean if two lines are the same line?

Back

If two lines are the same line, they have the same slope and y-intercept, meaning they coincide at all points.

Front

What does it mean if two lines intersect at one point?

Back

If two lines intersect at one point, it means the system of equations has one unique solution.

Front

What is the y-intercept of the line represented by the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point where the line crosses the y-axis.

Front

How can you determine the solution to a system of equations graphically?

Back

The solution is the point where the two lines intersect on the graph.

Front

What is the slope of the line represented by the equation y = -4x + 5?

Back

The slope is -4.

Front

If a system of linear equations has no solution, what does this indicate about the lines?

Back

It indicates that the lines are parallel and will never intersect.

Front

What is the slope-intercept form of the equation -8x + 2y = 4?

Back

The slope-intercept form is y = 4x + 2.