Understanding Slopes and Lines

The video tutorial covers solving various problems related to linear equations and graphs. It starts with identifying the equation of a line from a graph by determining the y-intercept and slope. It then moves on to finding points on a line by substituting values into the equation. The tutorial also includes deriving the equation of a line given a slope and a point, determining a cost function from a table, and finding the equation of a linear function from a table. Finally, it compares two lines to determine if they are perpendicular by analyzing their slopes.

What is the y-intercept of a line if the equation is y = 2x?

• 3

• 0

• 1

• 2

If a line has a slope of 2, what is the equation of the line passing through the origin?

• y = 2x + 1

• y = x + 2

• y = x

• y = 2x

Which point lies on the line defined by the equation 3x + 6y = 2?

• (1, 1)

• (0, 6)

• (1, -1/6)

• (0, 2)

What is the y-intercept of the line with the equation y = 4x - 22?

• 22

• 0

• 4

• -22

Given a slope of 4 and a point (3, -10), what is the equation of the line?

• y = 3x + 10

• y = 4x - 22

• y = 3x - 10

• y = 4x + 22

If the cost of renting a bicycle is a linear function of hours, what is the slope if the cost changes from 15 to 30 as hours increase from 2 to 5?

• 10

• 3

• 15

• 5

What is the equation of a line with a slope of 3 and passing through the point (1, 1)?

• y = 2x + 3

• y = 3x + 2

• y = 3x - 2

• y = 2x - 3

How do you determine if two lines are perpendicular?

• They have the same slope

• Their slopes are negative reciprocals

• Their x-intercepts are equal

• They have the same y-intercept

What is the slope of the line given by the equation 6x + 5y = 3?

• -6/5

• 5/6

• -5/6

• 6/5

If line l has a slope of -6/5, what is the slope of a line perpendicular to it?

• 5/6

• -5/6

• -6/5

• 6/5