Topic: 1. Parallel & Perpendicular Lines 2. Scatter Plots & Trend Lines Name: Date: Period: Essential Question: Vocabulary: Parallel Lines are lines in the same plane that do not intersect and have the same slope. 1. How can you determine if a line is parallel, perpendicular, or neither? 2. How can you determine whether two sets of data are related?
Slope-Intercept Form Useful for graphing since m is the slope and b is the y-intercept Point-Slope Form Use this form when you know a point on the line and the slope Also can use this version if you have two points on the line because you can first find the slope using the slope formula and then use one of the points and the slope in this equation. Standard Form Commonly used to write linear equation problems or express answers The slope is a number that tells "how steep" the line is and in which direction *Reminder:
Graphs of Parallel Lines The red line is the graph of y = – 4x – 3 and the blue line is the graph of y = – 4x – 7
Testing if Lines are Parallel Are the lines 12x + 3y = - 9 and -8x – 2y = 14 parallel? Are the lines y = 3x – 4 and y = 3x + 8 parallel? Are the lines y = 5x – 6 and y = 5x – 6 parallel?
Practice Testing if Lines are Parallel 1) y = - 2x – 4 and 2) 4y = x + 5 and 12y – 3x = 2
Find the equation of a line going through the point (3, -5) and parallel to
3) Find the equation of the line going through the point (4,1) and parallel to y = - 3x + 7
Vocabulary: Perpendicular Lines are lines in the same plane that intersect at right angles and have opposite reciprocals slope.
Graphs of Perpendicular Lines The red line is the graph of y = – 2x + 5 and the blue line is the graph of y = 1 / 2 x +4
Finding Opposite Reciprocals a)-3 b)1/3 c)-2/5 d)6 e)-3/2 f)-1/6 g)8 h)3/8 i)7/3
Testing if Lines are Perpendicular
Practice Testing if Lines are Perpendicular 4)
Find the equation of a line going through the point (3, -5) and perpendicular to
5) Find the equation of the line going through the point (4,1) and perpendicular to y = - 3x + 7 6) Find the equation of the line going through the point (-2,7) and perpendicular to
From the given equations, determine if the corresponding lines are parallel, perpendicular, or neither. y = 2x + 2 y = 4x - 2 2x + 6y = 1 4x + 12y =3 neither perpendicular parallel
Quick Review: Steps for determining if graphs are parallel or perpendicular 1.Put both equations into slope-intercept form. (Isolate for y ---- if ‘mx’ is on the side of the y move to the other side, then divide everything by value in front of ‘y’) 2.Find the slope and y-intercept of each equation. 3.Analyze the slope and y-intercept Parallel – Slope is the same; y-intercept different Perpendicular – Slope is a opposite reciprocal Wrap-Up:
Parallel Lines Perpendicular Lines
Independent Practice: Page 330 (1-6)
A scatter plot is a graph with points plotted to show a possible relationship between two sets of data. VOCABULARY: Ex: The table shows the number of cookies in a jar from the time since they were baked. Graph a scatter plot using the given data.
A correlation describes a relationship between two data sets. A graph may show the correlation between data. The correlation can help you analyze trends and make predictions. There are three types of correlations between data.
It is often helpful to add a line to better describe a scatter plot. This line, called a trend line, helps show the correlation between data sets more clearly. It can also be helpful when making predictions based on the data. An accurate trend line should fit the data closely. There should be about the same number of points above the line as below it. How do I write an equation? Slope Point Slope
Practice: a.Graph the (ages, grades) data of some students in a school. b.Draw a trend line. c.Find the equation of the line of best fit.
Wrap-Up: Fraction Review Vocabulary Review Summary Home-Learning Assignment #5 3 fraction problems (assigned in class) Page 331 (8, 14, 16, 18, 20) Page 337 (1, 2)