Understanding Perpendicular Lines and Point-Slope Form

The video tutorial explains how to write the equation of a line that is perpendicular to a given line and passes through a specific point. It covers the concept of opposite reciprocal slopes, the use of point-slope form, and the simplification of equations using the distributive property. The final equation is derived by ensuring the line passes through the given point and has the correct slope.

What is the slope of the given line y = -4/5x - 4?

• -4/5

• 4/5

• 5/4

• -5/4

What is the relationship between the slopes of perpendicular lines?

• They are equal

• They are unrelated

• They are negative reciprocals

• They are positive reciprocals

If the slope of one line is -4/5, what is the slope of a line perpendicular to it?

• -5/4

• 5/4

• -4/5

• 4/5

In point-slope form, what do x1 and y1 represent?

• The y-intercept of the line

• A specific point on the line

• Any point on the line

• The slope of the line

What is the point-slope form of a line?

• y = mx + b

• y - y1 = m(x - x1)

• y = m(x - x1) + b

• y = mx + c

What is the first step in converting the point-slope form to slope-intercept form?

• Convert the slope to a fraction

• Distribute the slope

• Isolate the y variable

• Add the y1 value to both sides

What operation is performed after distributing the slope in the point-slope form?

• Subtracting the x1 value from both sides

• Dividing both sides by the slope

• Adding the y1 value to both sides

• Multiplying the slope by x

How do you convert a whole number to a fraction?

• Add the numerator and denominator

• Divide by 2

• Multiply by 1

• Multiply by the denominator over itself

What is the final y-intercept of the line in the given problem?

• 15/4

• 5/4

• 16/4

• 31/4

What is the final equation of the line that is perpendicular to y = -4/5x - 4 and passes through (-3, 4)?

• y = 5/4x + 31/4

• y = -5/4x + 31/4

• y = -4/5x + 31/4

• y = 4/5x + 31/4