Lesson 6.1 Linear Equation Review
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1 Name: Lesson 6.1 Linear Equation Review Vocabulary Equation: a math sentence that contains Linear: makes a straight line (no Variables: quantities represented by (often x and y) Function: equations can sometimes be written as functions as well (using Cartesian Coordinates: to represent an equation with two variables with points (x,y) on a. x-axis: is a number line, with positive values to the right and negative to the left y-axis: is a number line, with positive values going up and negative going down Origin: the of the graph is called the origin Quadrants: A graph has four quadrants, usually labeled with, as follows
2 Assignment: A. Matching Equation Expression Function Equation Expression Function 2x + 3 f(x) = 2x + 3 y = 2x + 3 4x 2y = 0 f(x) = 2x 4x 2y B. Is it linear? Yes or No y = 2x + 3 y = 2x y = 1 2 x + 3 y = 2x y = 0.5x y = x a = 2b + 3 y = 2x + 3 y = 2x + 3 y = 2 x + 3 y = x C. Cartesian Coordinates - Label each coordinate on the graph: (7,4), (-5,3), (-4,-8), (6,-2), (0,9), (-1,0)
3 Vocabulary x-intercept: where the line crosses the y-intercept: where the line crosses the Example of a linear equation graph: Notice the arrows indicate that the lines continue forever (to infinity?) y-intercept = x-intercept = The graph goes through quadrants but not quadrant Does the graph go through the point (4,1)? Does the graph go through the point (2,-3)? Does the point (-4,7) satisfy the linear equation?
4 Assignment: y-intercept = x-intercept = Quadrants: Do the points satisfy equation? (-3,0)? (2,2)? (-1,-4)? y-intercept = x-intercept = Quadrants: Do the points satisfy equation? (-1,1)? (2,3)? (-4,0)? y-intercept = x-intercept = Quadrants: Do the points satisfy equation? (5,1)? (-2,-1)? (2,7)?
5 Substitution: An algebra technique Example: Equation: y + 2x = 3 If x=1, then what is y? Equation: y + 2x = 3 If y=0, then what is x? Assignment: 1) Equation: 2x + y = 4 If y=0, then what is x? 2) Equation: 3x 1 y = 9 If y=0, then what is x? 2 3) Equation: 3x + 2y = 6 If x=0, then what is y? 4) Equation: 3x + 2y = 5 If x=0, then what is y? 5) Equation: y = 2x + 3 If y=0, then what is x?
6 Graphing Method #1 Using intercepts STEP #1: Find the and plot these points. To find the y-intercept, set To find the x-intercept, set STEP #2: Find a third point by picking a random x-value and find the corresponding y-value by substitution STEP #3: Plot these three points and sketch the straight line through these points. Note: If the three points do not make a straight line then a mistake was made. 4 y-intercept x-intercept -4
7 Example a) 3x + 2y = 6 b) 5x + 2y 15 = 0
8 Assignment: Graph each equation using the intercept method. Show your work. 1) 2x y = 6 2) 2x + 3y = 6
9 3) 2x + y = 4 4) y = 2x 1
10 Practice Quiz: 1) Is it a linear equation? a) x + 2y = 2 b) 0.5x + 2.1y = ( 3) 2 c) y = 2x ) Analyze the linear graph y-intercept = x-intercept = Quadrants: Do the points satisfy equation? (-3,0)? (2,2)? (-1,-4)? 3) Equation: 1 x + y = 4 If y=0, then what is x? 2 4) Graph the following equation using the intercept method. Show your work. x + 2y = 2
11 Lesson 6.1 Linear Equation Review (teacher) Vocabulary Equation: a math sentence that contains an equals sign Linear: makes a straight line (no exponents on variables) Variables: unknown quantities represented by letters (often x and y) Name: Function: equations can sometimes be written as functions as well (using f(x) instead of y) all linear equations can be functions except for a vertical line. Cartesian Coordinates: to represent an equation with two variables with points (x,y) on a graph. x-axis: is a horizontal number line, with positive values to the right and negative to the left y-axis: is a vertical number line, with positive values going up and negative going down Origin: the centre of the graph is called the origin (0,0) Quadrants: A graph has four quadrants, usually labeled with Roman numerals, as follows
12 Vocabulary x-intercept: where the line crosses the x-axis (or where y=0) y-intercept: where the line crosses the y-axis (or where x=0) Example of a linear equation graph: Notice the arrows indicate that the lines continue forever (to infinity?) y-intercept = x-intercept = The graph goes through quadrants but not quadrant Does the graph go through the point (4,1)? Does the graph go through the point (2,-3)? Does the point (-4,7) satisfy the linear equation?
13 Graphing Method #1 Using intercepts STEP #1: Find the x and y-intercepts and plot these points. To find the y-intercept, set x = 0 then solve for y. To find the x-intercept, set y = 0 then solve for x. STEP #2: Find a third point by picking a random x-value and find the corresponding y-value by subbing into the function. STEP #3: Plot these three points and sketch the straight line through these points. Note: If the three points do not make a straight line then a mistake was made. 4 y-intercept x-intercept -4
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