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Math 71. 2.5 – The Point-Slope Form of the Equation of a Line. Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation: .

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## Math 71

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**Math 71**2.5 – The Point-Slope Form of the Equation of a Line**Suppose we know a point on a line is , and the slope of that**line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line.**Suppose we know a point on a line is , and the slope of that**line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line.**Suppose we know a point on a line is , and the slope of that**line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line.**Suppose we know a point on a line is , and the slope of that**line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line. point-slope form**Suppose we know a point on a line is , and the slope of that**line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line. point-slope form**Suppose we know a point on a line is , and the slope of that**line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line. point-slope form point**Suppose we know a point on a line is , and the slope of that**line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line. point-slope form point slope**Ex 1.Write the point-slope form of the equation of the line**with slope 3 that passes through the point Now write the equation in slope-intercept form. Ex 2.A line passes through the points and . Find an equation of the line in point-slope form. Now write the equation in slope-intercept form.**Nonintersecting lines that lie in the same plane are called**__________________________.**Nonintersecting lines that lie in the same plane are called**__________________________. parallel lines**What can you say about the slopes of parallel lines?**If two lines have the same slope, are they guaranteed to be parallel?**What can you say about the slopes of parallel lines?**If two lines have the same slope, are they guaranteed to be parallel? They’re the same.**What can you say about the slopes of parallel lines?**If two lines have the same slope, are they guaranteed to be parallel? They’re the same. Yes!**Ex 3.Write an equation of the line passing through and**parallel to the line whose equation is . Express the equation in point-slope form.**Lines that intersect at a right angle () are called**__________________________________.**Lines that intersect at a right angle () are called**__________________________________. perpendicular lines**What is the slope of line m?**What is the slope of line n? What happens when you multiply the slopes?**What is the slope of line m?**What is the slope of line n? What happens when you multiply the slopes?**What is the slope of line m?**What is the slope of line n? What happens when you multiply the slopes?**What is the slope of line m?**What is the slope of line n? What happens when you multiply the slopes?**What is the slope of line m?**What is the slope of line n? What happens when you multiply the slopes?**What is the slope of line m?**What is the slope of line n? What happens when you multiply the slopes? Slopes of perpendicular lines are negative reciprocals**In general, product of slopes of two nonvertical**perpendicular lines is ________. In other words, slopes of two nonvertical perpendicular lines are _____________________________. For example, if a line has slope , then any perpendicular line will have slope ______.**In general, product of slopes of two nonvertical**perpendicular lines is ________. In other words, slopes of two nonvertical perpendicular lines are _____________________________. For example, if a line has slope , then any perpendicular line will have slope ______.**In general, product of slopes of two nonvertical**perpendicular lines is ________. In other words, slopes of two nonvertical perpendicular lines are _____________________________. For example, if a line has slope , then any perpendicular line will have slope ______. negative reciprocals**In general, product of slopes of two nonvertical**perpendicular lines is ________. In other words, slopes of two nonvertical perpendicular lines are _____________________________. For example, if a line has slope , then any perpendicular line will have slope ______. negative reciprocals**Ex 4.Find the slope of any line that is perpendicular to the**line whose equation is .**Ex 5.Write the equation of the line passing through and**perpendicular to the line whose equation is . Express the equation in point-slope form and slope-intercept form.**Summary**point-slope form: parallel same slope(also two vertical lines are parallel) perpendicular slopes are negative reciprocals(also, vertical and horizontal lines are perpendicular)

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