Understanding Perpendicular Lines and Slope-Intercept Form

The video tutorial explains how to write new equations of lines in slope-intercept form, focusing on finding perpendicular lines. It covers the concept of opposite reciprocal slopes and demonstrates how to calculate the new slope and y-intercept using a given point. The tutorial concludes by finalizing the equation with the new values.

What is the general form of a line in slope-intercept form?

• y = mx + b

• y = x^2 + bx + c

• y = ax^2 + bx + c

• y = a/x + b

What is the relationship between the slopes of perpendicular lines?

• They are both negative

• They are opposite reciprocals

• They are equal

• They are both positive

If a line has a slope of -2, what is the slope of a line perpendicular to it?

• -2

• 1/2

• -1/2

• 2

Why can't we assume the y-intercept of a perpendicular line is the same as the original line?

• Because the x-intercept changes

• Because the line equation changes

• Because the slopes are different

• Because the y-intercept depends on the specific line

What is the first step in finding the y-intercept of a new line?

• Guess the y-intercept

• Plug in a point into the equation

• Change the slope

• Use the original line's y-intercept

When given a point (-3, -2), how do you use it to find the y-intercept?

• Subtract them

• Add them together

• Plug -3 into x and -2 into y

• Plug -3 into y and -2 into x

What is the value of b if the equation is y = 1/2x + b and the point (-3, -2) is on the line?

• -1/2

• 0

• -2

• 1/2

What is the final equation of the line after finding the y-intercept?

• y = -1/2x + 1/2

• y = -1/2x - 1/2

• y = 1/2x - 1/2

• y = 1/2x + 1/2

Why is it important to convert fractions to decimals when solving equations?

• It makes calculations easier

• It changes the equation

• It is a rule in mathematics

• It is required by the formula

What is the significance of the y-intercept in the equation of a line?

• It is where the line crosses the y-axis

• It determines the slope

• It changes the slope

• It is where the line crosses the x-axis