Graphing Linear Equations and Systems

The video tutorial explains how to solve a system of linear equations by graphing. It demonstrates graphing two linear equations on the same coordinate plane and interpreting the results. The first equation is converted to slope-intercept form and graphed, followed by the second equation. Both lines are found to be parallel, indicating no solution to the system. The tutorial concludes by explaining that such a system is inconsistent.

What is the first step in solving a system of linear equations by graphing?

• Calculate the determinant of the system.

• Graph both equations on the same coordinate plane.

• Find the solution algebraically.

• Determine the x-intercepts of both equations.

How do you convert the equation -3y + 9x = 18 into slope-intercept form?

• Divide both sides by 9.

• Multiply both sides by 3.

• Subtract 9x from both sides and divide by -3.

• Add 9x to both sides.

What is the slope of the line represented by the equation y = 3x - 6?

• -6

• -3

• 3

• 1/3

What is the y-intercept of the line y = 3x - 6?

• (3, 0)

• (0, -6)

• (0, 3)

• (-6, 0)

What is the slope of the line y = 3x + 2?

• 3

• 2

• -3

• -2

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

• (0, -2)

• (-2, 0)

• (2, 0)

• (0, 2)

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

• They coincide and have infinite solutions.

• They are perpendicular.

• They intersect at one point.

• They are parallel and have no solution.

What is the term used to describe a system of equations with no solution?

• Inconsistent

• Dependent

• Independent

• Consistent

If a system of equations is inconsistent, what should be entered in the solution box?

• DNE

• 0

• Infinity

• 1

What is the graphical representation of a system with no solution?

• Perpendicular lines

• Coinciding lines

• Parallel lines

• Intersecting lines