# 2.4 Essential Questions What is the point-slope form?

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2.4 Essential Questions What is the point-slope form?
How do you write an equation if you are given a slope and y-intercept? How do you write an equation if you are given a point and a slope? How do you write an equation that is parallel or perpendicular to a given line if you are only given a point? How do you write an equation if you are given two points?

2.4 Write Equations of Lines
Point-slope form Slope – intercept form y = mx + b y – y1 = m(x – x1)

Writing an equation given the slope and y-intercept
Write an equation of the line shown. From the graph, you can see that the slope is m = and the y-intercept is b = – 2. 3 4 y = mx + b Use slope-intercept form. y = x + (– 2) 3 4 Substitute for m and –2 for b. 3 4 3 4 y = x – 2 Simplify.

Writing an equation given the slope and y-intercept
m = 3, b = 1 Use slope – intercept form y = mx + b y = x + 1 3 y = x + 1 3

Writing an equation given the slope and y-intercept
GUIDED PRACTICE m = – 2 , b = – 4 y = mx + b y = – 2x + (– 4 ) y = – 2x – 4

Writing an equation given the slope and y-intercept
GUIDED PRACTICE m = – b = 3 4 7 2 y = mx + b y = – x + 3 4 7 2

Writing an equation given the slope and a point
EXAMPLE 2 Writing an equation given the slope and a point Write an equation of the line that passes through (5, 4) and has a slope of – 3. Because you know the slope and a point on the line, use point-slope form to write an equation of the line. y – y1 = m(x – x1) point-slope form. Let (x1, y1) = (5, 4) and m = – 3. y – 4 = – 3(x – 5) y – 4 = – 3x + 15 y = – 3x + 19

Writing an equation given the slope and a point
GUIDED PRACTICE GUIDED PRACTICE Write an equation of the line that passes through (– 1, 6) and has a slope of 4. y – y1 = m(x – x1) y – 6 = 4(x – ( – 1)) y – 6 = 4x + 4 y = 4x + 10

How to write equations of parallel or perpendicular lines
EXAMPLE 3 (use the point-slope form) Write an equation of the line that passes through (–2,3) and is parallel to the line y = –4x + 1. The given line has a slope of m = –4. So, a line parallel to it has the same slope of –4. Now you know the slope and a point on the line, so use the point-slope form with (x1, y1) = (– 2, 3) to write an equation of the line. y – y1 = m2(x – x1) y – 3 = – 4(x – (– 2)) y – 3 = – 4(x + 2) y – 3 = – 4x – 8 y = – 4x – 5

How to write equations of parallel or perpendicular lines
EXAMPLE 3 How to write equations of parallel or perpendicular lines Write an equation of the line that passes through (–2,3) and is perpendicular to the line y = –4x + 1. 1 4 A line perpendicular to a line with slope m = – 4 has a slope of y – y1 = m2(x – x1) y – 3 = (x – (– 2)) 1 4 y – 3 = (x +2) 1 4 y – 3 = x + 1 4 2 y = x + 1 4 2

How to write equations of parallel or perpendicular lines
GUIDED PRACTICE GUIDED PRACTICE Write an equation of the line that passes through (4, –2) and is parallel to the line y = 3x – 1. A parallel slope would be 3. y – y1 = m2(x – x1) y – (– 2) = 3(x – 4) y + 2 = 3(x – 4) y + 2 = 3x – 12 y = 3x – 14

How to write equations of parallel or perpendicular lines
GUIDED PRACTICE Write an equation of the line that passes through (4, –2) and is perpendicular to the line y = 3x – 1. 1 3 A perpendicular slope is – y – y1 = m2(x – x1) y – (– 2) = – (x – 4) 1 3 y + 2 = – (x – 4) 1 3 4 3 y + 2 = – x + 1 y = – x – 1 3 2

How to write an equation given two points
Write an equation of the line that passes through (5, –2) and (2, 10). First, find the slope y2 – y1 m = x2 –x1 = 10 – (– 2) 2 – 5 12 – 3 = = – 4 Now you know the slope and two points on the line, so use point-slope form with either given point to write an equation of the line. y2 – y1 = m(x – x1) y – 10 = – 4(x – 2) y – 10 = – 4x + 8 y = – 4x + 18

How to write an equation given two points
GUIDED PRACTICE GUIDED PRACTICE Write an equation of the line that passes through the given points. (– 2, 5), (4, – 7) Find the slope m – 7 – 5 = 4 – (– 2) = – 2 Use that slope and one of the two points to find the equation of the line. y – y1 = m(x – x1) y – 7 = – 2(x – 4) y – 7 = – 2 (x – 4) y + 7 = – 2x + 8 y = – 2x + 1

How to write an equation given two points
GUIDED PRACTICE GUIDED PRACTICE Write an equation of the line that passes through (6, 1), (–3, –8) m = – 8 – 1 – 3 – 6 – 9 = = 1 y – y1 = m(x – x1) y – (– 8)) = 1(x – (– 3)) y + 8 = 1 (x + 3) y + 8 = x + 3 y = x – 5

How to write an equation given two points
GUIDED PRACTICE Write an equation of the line that passes through (–1, 2), (10, 0) m = 0 – 2 10– (– 1) 2 11 = y – y1 = m(x – x1) y – 0 = (x – 10) 2 11 y = (x – 10) 2 11 y = 2 11 x + 20

HOMEWORK 2.4 p. 101 #3-16(EOP); 17, 20-25, 30-38, 40-45