Finding Equations of Parallel and Perpendicular Lines

The video tutorial covers the slope-intercept form of a line, explaining its usefulness in graphing due to the easy identification of the y-intercept. It delves into the concepts of parallel and perpendicular slopes, highlighting that parallel lines have equal slopes while perpendicular lines have slopes that are opposite reciprocals. The tutorial provides a step-by-step guide to writing equations in slope-intercept form for lines that are parallel or perpendicular to a given line through a specific point. Practice problems are included to reinforce the concepts discussed.

Why is the slope-intercept form particularly useful for graphing?

• It gives a clear y-intercept which is easy to plot.

• It makes it easy to find the slope.

• It simplifies the equation.

• It provides the x-intercept directly.

In the slope formula, what does 'm' represent?

• The y-intercept

• The coefficient of x

• The x-intercept

• The constant term

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

• The point where the line crosses the x-axis

• The point where the line crosses the y-axis

• The slope of the line

• The coefficient of x

What must be true for two lines to be parallel?

• They must be vertical.

• They must have the same slope.

• They must intersect at one point.

• They must have different slopes.

What is the relationship between the slopes of two perpendicular lines?

• They are negative reciprocals of each other.

• They are equal.

• They are both negative.

• They are both positive.

What is the first step in writing an equation of a line in slope-intercept form that is parallel or perpendicular to a given line?

• Find the y-intercept.

• Make the slope a fraction.

• Determine the x-intercept.

• Solve for y.

If a line has a slope of 3, what is the slope of a line perpendicular to it?

• -1/3

• -3

• 1/3

• 3

What is the final step in converting a point-slope form equation to slope-intercept form?

• Combine like terms to find the y-intercept.

• Add the y-value.

• Subtract the x-value.

• Distribute the slope.

What is the equation of a line parallel to y = -5x - 3 through the point (-5, 7)?

• y = 5x + 2

• y = -5x - 2

• y = -5x + 2

• y = 5x - 2

What is the equation of a line perpendicular to y = 1/5x + 4 through the point (4, 4)?

• y = 5x - 16

• y = -5x + 24

• y = 5x + 24

• y = -5x - 16