Linear Topics Notes and Homework DUE ON EXAM DAY. Name: Class period:

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1 Linear Topics Notes and Homework DUE ON EXAM DAY Name: Class period: Absolute Value Axis b Coordinate points Continuous graph Constant Correlation Dependent Variable Direct Variation Discrete graph Domain Displacement Section Vocabulary -- Make sure you know it. It is sad to fail an exam because of vocabulary Function f(x) Independent Variable k Linear Line of Best Fit m Midpoint Mean Measure Central Tendency (MCT) Median Mode Non Proportionate equation Origin Parallel Parent Functions Parent graph Perpendicular Predictor Proportionate Equation Quadrants Quadratic Range (graphing) Range (MCT) Rate of Change Reflection Regression Rotation Scatter plot Slope Slope Intercept Form Standard Form Translation Trend Variable Vertical Line Test Vertices (vertex) Volume X Intercept Y Intercept 1

2 Functions Other terms for y f(x), f(a) f(any variable that is in the equation) Examples: List b, the y intercept: y= 3x +4 (, ) f(x) =3x + 4 (, ) f(a)= 3a - 2 (, ) f(m)=2m (, ) Y = mx +b b is the y intercept Y = mx +b Functions slope y intercept misc stuff The y intercept is the point where the graph goes through the Y axis!!!!! b is a number. There is NEVER a letter next to it!!!!! If an equation does not have a b, then the graph goes through the origin. (0,0) The y intercept coordinate point ALWAYS~ starts with a zero. In the above equations, circle b and write b as a coordinate point. m= SLOPE (circle slope in the examples to the left) M is always next to a letter. No exceptions. y=3x 3= slope Y=3x+4 3 = slope 4 = y intercept. Slope means the slant of the line. Other terms for slope: Rise y y2 y1 rate of change Run x x2- x1 There is NO excuse on a TAKS test to forget that slope is y over x. On the formula chart, it gives the slope formula that shows it is y over x. Do not guess look it up. Y = 3x slope is POSITIVE Y= -3x slope is NEGATIVE Y = 4 slope is ZERO - there is no x. The line is horizontal X = 3 There is no y. There is no slope. This is a vertical line (slope is undefined!!) What is a function? It must pass the vertical line test. If you draw a vertical line on any graph, it cannot touch two points or it is NOT a function. In other words, no two points can have the same X value. 2

3 Graphing For the following equations, put a box around the slope and a circle around the y intercept. Remember, slope is a number. It does not include a variable!!!!!!!!!!!!!!! The y intercept is a constant it never has a variable next to it!!!!!!! You may have to put the equation into y =mx+b form. y= 2 x + 5 y = 4 y=-x y = ½ x 3 y = 3 ½ x ¾ x + 4 = y y = 4x x = 5 -x = y + 5 4x y = 5 y = x y =0 Graphing linear equations Form y = mx +b 1. Find the y intercept. Mark it on the graph. 2. Find the slope. Determine the rise and the run. 3. Start at the y intercept and follow your rise over run to the second point. Connect the dots. If the equation has no y intercept where do you start? Graph y = x Graph y=-x Graph y = ½ x Graph y = - ½ x Graph y = 2x Graph y = - 2x Graph on your calculator to compare What is the slope of y= x? How did the graphs of y = x and y =-x compare? How did the graph of y = x and y = ½x compare? How did the graph of y = x and y = 2x compare? How did the graph of y = ½ x and y = 2x compare? What conclusion can you draw about the effect of a slope where the absolute value is less than 1 and a slope where the absolute value is larger than 1 on a graph? So, the effect of slope on a line graph is to (In effect, it rotates around the origin and the negative sign reflects it) 3

4 Graph y = x + 2 y = x +4 y = x - 3 y = x - 2 Did the slope change? What did happen? And when the slope does not change the lines are Graph y = -x +2 y = -x +4 y = -x - 2 y = -x - 4 What can we conclude the effect of changing the y intercept is on a graph, if the slope does not change? and the lines are (in effect this is a translation) Quadrants: Shaped like a C II I III IV Label the graph above. In quad I x values are and y values are (, ) In quad II the x values are and they values are (, ) In quad III x values are and y values are (, ) In quad IV the x values are and they values are (, ) Label on the graph Domain and range. Continuous graph like above (smallest x < x < largest x ) Find the smallest x Find the largest x ( < x < ) If your x value has an open circle at it, you do not put an = sign under the < or <. If the circle has a filled in circle (or if it touches the point), put the = sign under the <. Do the same for the y values ( < y < ) low y high y On scatter plots, you just list your points: { x =,,,, } { y =,,,, } Don t repeat values

5 Slope Intercept and Standard Form of a Linear Equation Standard Form: Slope Intercept Form: Ax + By = C y = mx +b In Standard x and y must be on one side of the = sign and the number on the other. Once in standard form Slope = - A Y intercept = C B B X Intercept = C A y = - A x + C B A Example: 2y = 4x +8 Standard Form: -4x +2y = 8 (WHY?) A = B= C= So slope = y intercept = Solving for y, we get: 4x 2y 8 4x 4x 1 2y 2 y 2x x 8 What is the slope? What is the y intercept? You do it: -4x + 6y = x = 3y If you can t remember this, then write in slope intercept form, or just solve the equation for y. -3x -4 = 6y 8x +3 = 6y 5

6 YOU MUST LEARN THESE! YOU WILL BE TESTED OVER AND OVER The parent graph of linear equations y x 2 The parent quadratic is y x The parent absolute value is y x Y = # Graph of a number with no x. y= x Absolute value parent function y = x Parent linear function y = x 2 Parent quadratic function 6

7 Show all work!!!!!! Homework Change from Standard to Slope Intercept Form and state the slope and the y intercept 1. -3x + 5y = x - 4y = x 2y =12 Y= Y= Y= m= b = m= b = m= b = 4. 3x + 7y = x -4y = x + 18y =21 Y= Y= Y= m= b = m= b = m= b = 7. 3 y =8 8. 6x = x = 2y + 6 Y= Y= Y= m= b = m= b = m= b = 7

8 Put it all together 1. Label the Quadrants 2. Graph y = ½ x Change the y intercept to 2. Write your new equation and graph it. The two graphs are 4. Using the new equation, change the slope to negative. Write the new equation and graph it. This graph is a of the graph in #3. 5. Using the new equation, change the slope to -3, write the new equation and graph it. 6. Using the new equation, change the y intercept to -3, write the new equation and graph it. Lines in 5 and 6 are Change 4x -6y = 18 to slope intercept form Name Class period 8