Understanding Lines: Slopes and Relationships

This video tutorial teaches how to determine if two equations represent parallel, perpendicular, or neither type of lines by analyzing their slopes and y-intercepts. It covers converting equations to slope-intercept form, identifying parallel lines by equal slopes, and recognizing perpendicular lines through negative reciprocal slopes. Special cases involving horizontal and vertical lines are also discussed, along with coincident lines that overlap completely.

What is the first step in determining if two lines are parallel or perpendicular?

• Convert to standard form

• Identify the slopes

• Identify the y-intercepts

• Graph the lines

If two lines have the same slope but different y-intercepts, what is their relationship?

• They are perpendicular

• They are parallel

• They are coincident

• They intersect at a right angle

How do you convert an equation from standard form to slope-intercept form?

• Divide both sides by the slope

• Multiply both sides by the y-intercept

• Subtract the x-term from both sides

• Add the x-term to both sides

What is the relationship between two lines if their slopes are negative reciprocals?

• They are perpendicular

• They are parallel

• They are neither parallel nor perpendicular

• They are coincident

What is the product of the slopes of two perpendicular lines?

• 0

• 1

• Undefined

• -1

What do you call two lines with the same slope and y-intercept?

• Coincident lines

• Parallel lines

• Intersecting lines

• Perpendicular lines

What is the slope of a horizontal line?

• 0

• 1

• Undefined

• Infinity

What is the slope of a vertical line?

• 0

• 1

• Infinity

• Undefined

If a line is in the form y = constant, what type of line is it?

• Perpendicular line

• Vertical line

• Horizontal line

• Diagonal line

If a line is in the form x = constant, what type of line is it?

• Perpendicular line

• Diagonal line

• Horizontal line

• Vertical line