Packet: Lines (Part 1) Standards covered:
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1 Packet: Lines (Part 1) Standards covered: *(2)MA.912.A.3.8 Graph a line given any of the following information: a table of values, the x and y- intercepts, two points, the slope and a point, the equation of the line in slope- intercept form, standard form, or point- slope form. (Also assesses MA.912.A.3.12.) *(4)MA.912.A.3.9 Determine the slope, x- intercept, and y- intercept of a line given its graph, its equation, or two points on the line. (Also assesses MA.912.A.3.12.) *MA.912.A.3.12 Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph. (Assessed with MA.912.A.3.8, MA.912.A.3.9, MA.912.A.3.10, and MA.912.A.3.11.) Section 5 Lines (Part 1) 1
2 Section 5 Video 1 Lines, the Great Unknown Lets say you work the night shift, and make $11/hour. If you happened to get called in a night you are not working, you get $50 for just coming in. Hours worked: x Money Earned: Section 5 Lines (Part 1) 2
3 If you weigh 200 lbs and want to lose some weight You go on a diet and start losing, on average, 3lbs each week. Weeks on a diet: x Your weight: Important Equations Slope formula (on your reference sheet): slope = m =!!!!!!!!!! Forms of equations: Point Slope (on reference sheet): y y! = m x x! (for Standard Form) Slope Intercept (on reference sheet): y = mx + b Standard Form: Ax + By = C Section 5 Lines (Part 1) 3
4 Section 5 Video 2 Find Slope from a Graph, 2 Points, or an Equation Let s think about slope. Slope measures a graph s speed. Positive slope Negative Slope Zero Slope Study Edge Tip If you are not sure if the slope of a line is positive or negative, draw 2 vertical lines on each side. Ø If the graph makes the letter N, it has a Negative slope. Ø If the graph does not make the letter N, it has a positive slope. If you see two points on a graph, we call this method rise over run. slope = rise run Section 5 Lines (Part 1) 4
5 Try it! Section 5 Lines (Part 1) 5
6 Ø Slope formula (on your reference sheet): slope = m =!!!!!!!!!! Ø If you are given 2 points, label them (x!, y! ) and (x!, y! ), then plug in! Find the slope between the points (2, 5) and (- 3, 7) Try it! Find the slope between the points (- 3, 8) and (5, - 2) Section 5 Lines (Part 1) 6
7 Ø Find the slope of the line with the following equation: y = mx + b Ø If you have an equation, solve the equation for y. The coefficient of x will be the slope. y = 3x + 4 y + 7 = 2x Try it! y = 4 3 x + 3 2x + 3y = 4 Section 5 Lines (Part 1) 7
8 BEAT THE TEST! 1. Two points on a given path are (10,25) and (5,20). Find the slope of the path. Section 5 Lines (Part 1) 8
9 2. In a game, Ender needed to travel along the path 3x 4y = 10 in order to avoid his opponent. What was the slope of his course? A.!! B.!! C.!! D.!! Section 5 Lines (Part 1) 9
10 3. Enrique flew his model airplane with a slope of!. Which of the! following graphs could have been the flight path? A. C. B. D. Section 5 Lines (Part 1) 10
11 Section 5 Video 3 Find Intercepts from a Graph, 2 Points, Equation There are three different cases that we need to be able to find intercepts: 1. A Graph 2. An Equation 3. Two points 1. If you have a graph, just look where the line hits the x- axis and y- axis! Ø x- intercept o Where the line hits the x- axis (and y = 0) o Will be in the form (x, 0) Ø y- intercept o Where the line hits the y- axis (and x = 0) o Will be in the form (0,y) On the graph to the right, find the intercepts. x- int: y- int: Section 5 Lines (Part 1) 11
12 2. If you have an equation, Ø To find the y intercept, replace a 0 for x and solve for y Ø To find the x intercept, replace a 0 for y and solve for x Find the x and y intercepts: 2x + 5y = 10 Try it! Find the x and y intercepts: y = 3x + 2 Section 5 Lines (Part 1) 12
13 3. If you are given 2 points, we are going to use a couple of equations off your equation sheet!!! Ø First, find the slope: slope = m =!!!!!!!!!! Ø Use Point Slope form: y y! = m x x! Let s try the points (3, 2) and (1, - 1). Find the two intercepts. Try it! (4, - 2), (- 5, 3) Section 5 Lines (Part 1) 13
14 BEAT THE TEST! 1. A plane is currently at 200 ft and is descending at 10 feet per minute. The path of the gliding plane can be given by the following equation, y = 10x where y is the height of the plane and x is the number of minutes. In how many minutes will the plane land? (Hint: In other words, what is the x- intercept?) A. 10 B. 20 C. 100 D. 200 Section 5 Lines (Part 1) 14
15 2. What is the coordinate of the y intercept of the following graph? Round to the nearest integer. Section 5 Lines (Part 1) 15
16 3. Given the following equation, Find the x- intercept. 2x + 5y = A graph goes through the points (1,1) and (- 5,5). What is the y- intercept? Section 5 Lines (Part 1) 16
17 Section 5 Video 4 Make a Graph from Points and/or Slope Ø Plot the two points and draw a line through them. Draw a line through the points (1,5) and (4,- 3) Ø Sometimes you are given a point and a slope Suppose a line goes through the point (2,1) and has a slope of!! 1. P the point you know 2. Use the slope to draw another point, using slope = rise run 3. Draw a line through the two points Section 5 Lines (Part 1) 17
18 BEAT THE TEST! 1. A line has an x intercept of 3 and a slope of!. Which graph! represents the line? A. C. B. D. Section 5 Lines (Part 1) 18
19 2. A surveyor s line goes through a special set of coordinates at (- 2,4) and (2,- 1) Which of the following could be the graph? A. C. B. D. Section 5 Lines (Part 1) 19
20 Section 5 Video 5 Identify a Graph from an Equation If you have an equation, you can identify the graph a couple of ways Ø We will be focused on drawing lines here, and later you will be identifying lines Intercepts Method Ø Replace x with 0 and solve for y. That s the y intercept! Ø Replace y with 0 and solve for x. That s the x intercept! Ø Plot the intercepts and draw a line through them 2x 3y = 6 Section 5 Lines (Part 1) 20
21 Try it! 8x = 12 4y Slope Intercept Method y = mx + b 1. Solve the equation for y. 2. The y intercept is b, plot that point. 3. The slope is m, use rise over run to plot the second point. y = 2x + 1 Section 5 Lines (Part 1) 21
22 Try it! x + y = 1 Section 5 Lines (Part 1) 22
23 BEAT THE TEST! 1. Which is the graph of the following equation? 2x 5y = 10 A. C. B. D. Section 5 Lines (Part 1) 23
24 2. Which of the following graph could represent the equation below? y = 35x A. C. B. D. Section 5 Lines (Part 1) 24
25 Section 5 Lines (Part 1) 25
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