Understanding Area of a Bounded Region

The video tutorial explains how to find the area of a region bounded by the y-axis, a linear function F(x) = -1/3x + 6, and a line perpendicular to F(x) passing through the origin. It involves graphing the functions, determining the perpendicular line's equation, and calculating the area of the triangular region formed. The process includes solving for the intersection point of the two lines and using the area formula for a triangle to find the final area.

What are the boundaries of the region whose area we need to find?

• Two parallel lines and the x-axis

• A circle and a tangent line

• The y-axis, a linear function, and a line perpendicular to it

• The x-axis, a quadratic function, and a vertical line

What is the y-intercept of the function F(x) = -1/3x + 6?

• -1/3

• 3

• 6

• 0

How do you determine the slope of a line perpendicular to F(x) = -1/3x + 6?

• Subtract 1 from the slope of F(x)

• Use the negative reciprocal of the slope of F(x)

• Double the slope of F(x)

• Use the same slope as F(x)

What is the equation of the line perpendicular to F(x) and passing through the origin?

• G(x) = x/3

• G(x) = 3x

• G(x) = -1/3x

• G(x) = -3x

What shape is formed by the lines and the y-axis?

• Square

• Triangle

• Circle

• Rectangle

What is the length of the base of the triangular region?

• 12 units

• 9 units

• 6 units

• 3 units

How do you find the height of the triangle formed by the lines?

• By calculating the distance between the y-intercepts of the lines

• By using the y-intercept of F(x)

• By finding the x-coordinate of the intersection point of the lines

• By measuring the vertical distance from the x-axis

What is the x-coordinate of the intersection point of F(x) and G(x)?

• 3

• 9/5

• 1/3

• 6

What is the formula for the area of a triangle?

• Base x Height

• Base + Height

• Base - Height

• 1/2 x Base x Height

What is the area of the triangular region bounded by the lines?

• 5 square units

• 15 square units

• 27/5 square units

• 9 square units