Understanding Slope and Intercepts

The video tutorial explains how to solve a system of equations by graphing. It covers the process of converting equations to slope-intercept form, plotting them on a graph, and determining the solution based on the intersection of the lines. If the lines are parallel, the system has no solution and is classified as inconsistent. The tutorial provides a step-by-step guide to graphing each equation and understanding the implications of their slopes and intercepts.

What is the solution to a system of equations if the lines intersect at a point?

• The system has an infinite number of solutions.

• The system has no solution.

• The ordered pair of the intersection point is the solution.

• The lines are parallel.

How do you write the equation -x + y = 1 in slope-intercept form?

• y = -x + 1

• y = 1 + x

• y = x + 1

• y = 1 - x

What is the slope of the line represented by the equation y = x + 1?

• 1

• -1

• 2

• 0

When graphing the line y = x + 1, what is the y-intercept?

• (0, 0)

• (1, 0)

• (0, 1)

• (1, 1)

What is the slope of the line represented by the equation y = x - 4/3?

• -4/3

• 4/3

• -1

• 1

What is the y-intercept of the line y = x - 4/3?

• (0, 1)

• (0, -4/3)

• (0, 4/3)

• (0, 0)

What does it mean if two lines have the same slope but different y-intercepts?

• The lines are parallel.

• The lines intersect at one point.

• The lines form a right angle.

• The lines are coinciding.

If two lines are parallel, what can be said about the system of equations?

• The system is dependent.

• The system has one solution.

• The system has infinite solutions.

• The system has no solution.

What is the classification of a system of equations with no solution?

• Independent

• Inconsistent

• Dependent

• Consistent

What is the result of graphing two lines that are the same?

• The system is inconsistent.

• The system has infinite solutions.

• The system has one solution.

• The system has no solution.