Understanding Perpendicular Lines and Slopes

The video tutorial explains how to graph a line perpendicular to a given equation in standard form. It covers the properties of perpendicular lines, such as intersecting at a 90° angle and having opposite reciprocal slopes. The tutorial demonstrates converting an equation to slope-intercept form to find the slope and then finding the perpendicular slope. It also shows how to derive the equation of a perpendicular line that passes through a specific point using point-slope form.

What is a key characteristic of perpendicular lines?

• They have the same slope.

• They are parallel.

• They never intersect.

• They intersect at a 90° angle.

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

• Multiply both sides by the slope.

• Add the y-intercept to both sides.

• Subtract the x variable from both sides.

• Isolate the y variable.

What is the slope of the equation x + 2y = 3 when converted to slope-intercept form?

• -1/2

• 2

• -2

• 1/2

What is the alternative method to find the slope of a line in standard form?

• Use the formula A + B.

• Take the opposite of A over B.

• Multiply A and B.

• Divide A by B.

If the slope of a line is 1/2, what is the slope of a line perpendicular to it?

• 2

• -2

• -1/2

• 1/2

What is the point-slope form of a line?

• Ax + By = C

• y = mx + b

• y - y1 = m(x - x1)

• y = x + c

Which point does the new perpendicular line pass through?

• (3, 2)

• (2, 3)

• (1, 7)

• (0, 0)

What is the final equation of the perpendicular line derived in the tutorial?

• y = 2x - 9

• y = -2x + 9

• y = -2x - 9

• y = 2x + 9

Why is it important for the slopes of perpendicular lines to be opposite reciprocals?

• To ensure they are parallel.

• To ensure they never intersect.

• To ensure they intersect at a 90° angle.

• To ensure they have the same y-intercept.

What is the y-intercept of the final perpendicular line equation?

• 3

• 9

• 7

• 12