Geometry Warm ups What is the slope of the line MN for M(–3, 4) and N(5, –8)? What is the slope of a line perpendicular to MN for M(–3, 4) and N(5, –8)?

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Geometry Warm ups What is the slope of the line MN for M(–3, 4) and N(5, –8)? What is the slope of a line perpendicular to MN for M(–3, 4) and N(5, –8)? What is the slope of a line parallel to MN for M(–3, 4) and N(5, –8)?

A.B. C.D. Warm ups continued What is the graph of the line that has slope 4 and contains the point (1, 2)?

What is the graph of the line that has slope 0 and contains the point (–3, –4)? A.B. C.D. Warm ups continued

3-4 EQUATIONS OF LINES Objective: Write an equation of a line given information about the graph. Solve problems by writing equations.

Vocabulary slope-intercept form point-slope form

Concept

Example 1 Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Then graph the line. Slope and y-intercept y = mx + bSlope-intercept form y = 6x + (–3)m = 6, b = –3 y = 6x – 3 Simplify.

Example 1 Slope and y-intercept Answer: Plot a point at the y-intercept, –3. Use the slope of 6 or to find another point 6 units up and 1 unit right of the y-intercept. Draw a line through these two points.

TOO A.x + y = 4 B.y = x – 4 C.y = –x – 4 D.y = –x + 4 Write an equation in slope-intercept form of the line with slope of –1 and y-intercept of 4.

Example 2 Slope and a Point on the Line Point-slope form Write an equation in point-slope form of the line whose slope is that contains (–10, 8). Then graph the line. Simplify.

Example 2 continued Slope and a Point on the Line Answer: Graph the given point (–10, 8). Use the slope to find another point 3 units down and 5 units to the right. Draw a line through these two points.

TOO Write an equation in point-slope form of the line whose slope is that contains (6, –3). A. B. C. D.

Example 3 A. Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0). Two Points Step 1 First, find the slope of the line. Slope formula x 1 = 4, x 2 = –2, y 1 = 9, y 2 = 0 Simplify.

Example 3 continued Two Points Step 2 Now use the point-slope form and either point to write an equation. Distributive Property Add 9 to each side. Answer: Point-slope form Using (4, 9):

Example 3 B. Write an equation in slope-intercept form for a line containing (–3, –7) and (–1, 3). Two Points Step 1 First, find the slope of the line. Slope formula x 1 = –3, x 2 = –1, y 1 = –7, y 2 = 3 Simplify.

Example 3 Two Points Step 2 Now use the point-slope form and either point to write an equation. Distributive Property Answer: m = 5, (x 1, y 1 ) = (–1, 3) Point-slope form Using (–1, 3): Add 3 to each side. y = 5x + 8

Try with a Mathlete A. Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8). A. B. C. D.

TOO A.y = 2x – 3 B.y = 2x + 1 C.y = 3x – 2 D.y = 3x + 1 B. Write an equation in slope-intercept form for a line containing (1, 1) and (4, 10).

Example 4 Horizontal Line Write an equation of the line through (5, –2) and (0, –2) in slope-intercept form. Slope formula This is a horizontal line. Step 1

Example 4 Horizontal Line Point-Slope form m = 0, (x 1, y 1 ) = (5, –2) Step 2 Answer: Simplify. Subtract 2 from each side.y = –2

TOO Write an equation of the line through (–3, 6) and (9, –2) in slope-intercept form. A. B. C. D.

Horizontal and Vertical Lines

Homework Pg. 202 # 13 – 35 odd

Geometry Warm ups 1) Write two slopes that are parallel 2) Write two slopes that are perpendicular 3) Write two slopes that are neither 4) Write an equation in slope-intercept form of the line with slope -3 and y-intercept 7. 5) What is the slope of the line that goes through points (2, -5) and (4, -5)?

3 – 4 EQUATIONS OF LINES (DAY 2) Objective: To write equations of lines that are parallel and perpendicular to given lines.

Example 5 Write Equations of Parallel or Perpendicular Lines y =mx + bSlope-Intercept form 0 =–5(2) + bm = –5, (x, y) = (2, 0) 0 =–10 + bSimplify. 10 =bAdd 10 to each side. Answer: So, the equation is y = –5x + 10.

A.y = 3x B.y = 3x + 8 C.y = –3x + 8 D. Example 6

Example 7 Write an equation of a line that is parallel to the line through (4, 0). Write an equation of a line that is perpendicular to the line through (4, 0).

Example 8 A.C = 25 + d B.C = 125d C.C = 100d + 25 D.C = 25d RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit. Write an equation to represent the total cost C for d days of use.

Homework Pg. 203 # 37 – 42 all, 46 – 49 all, 58, 59