Graphing Systems

What is the relationship between the slopes of two lines that are perpendicular?

• The product of their slopes is 1.

• The product of their slopes is 0.

• The product of their slopes is -1.

• The product of their slopes is 2.

What is a system of linear equations?

• A set of two or more linear equations with the same variables.

• A single linear equation with multiple variables.

• A collection of nonlinear equations.

• A system of equations that has no solutions.

What is the graphical representation of a solution to a system of equations?

• The point where the lines intersect.

• The area between the lines.

• The slope of the lines.

• The distance between the lines.

What is the significance of the slope in a linear equation?

• It represents the rate of change of y with respect to x.

• It indicates the y-intercept of the equation.

• It shows the maximum value of y.

• It determines the direction of the graph.

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

• The equations represent different lines that intersect at one point.

• The equations represent the same line.

• The equations have no solutions at all.

• The equations represent parallel lines.

What does the term 'intersecting lines' imply in a system of equations?

• The system has no solution.

• The system has infinitely many solutions.

• The system has exactly one solution.

• The system has two solutions.

How do you find the x-intercept of a line?

• Set y = 0 in the equation and solve for x.

• Set x = 0 in the equation and solve for y.

• Find the slope of the line and use it to determine the intercept.

• Use the quadratic formula to find the x-intercept.

What is the y-intercept of the line given by the equation @@y = -\frac{1}{2}x + 4@@?

• 2

• 4

• 6

• 0

What does it mean if a system of equations has no solution?

• The lines are parallel and will never intersect.

• The lines intersect at one point.

• The lines coincide and have infinitely many solutions.

• The lines are perpendicular and intersect at a right angle.

What is the formula for the slope between two points (x1, y1) and (x2, y2)?

• @@m = rac{y2 - y1}{x2 - x1}@@

• @@m = rac{y1 - y2}{x2 - x1}@@

• @@m = rac{y2 + y1}{x2 + x1}@@

• @@m = rac{y2 - y1}{x1 - x2}@@