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(Slope (Different types of Linear equations (Point and the equation of a…

- - - - You can take the slope from the perpendicular line, and use the equation \( \frac{x^{-1}}{y^{-1}} \) to flip around the slope, and get the slope for the line you are trying to graph. Using the slope you can then plot the point and graph the line using the slope
    - - You can take the slope from the parallel line, because it will have the same slop since they are parallel. Using the slope you can then plot the point and graph the line using the slope you took from the line.
    - - Given (2,4) and (3,-2). \( \frac{y2-y1}{x2-x1} \) --> \( \frac{-2-4}{3-2} \)--> x= -6 plug in the slope y+2=-6(x-3)
    - - Using the slope you can plot the point and graph the line using the slope you took from the line.
    - - Using \( y=mx+b \), where \(m\) is the slope and \(b\) is the y-intercept
    - - Find the point that crossed the y-axis and use it as the y-intercept. Find two points on the line and either count the rise and run, or use \( \frac{y2-y1}{x2-x1} \)
- - - - \( f(x) = | x | \)
        
        \( f(x)= | x - 3 | + 6 \)
        
        https://drive.google.com/file/d/1bL5V6_OOya89e1348EG59OIupsTfO50j/view?usp=sharing This function shifts 6 units up and three units to the left
    - - \(f(x) = \frac{1}{x}\)
        
        \(f(x) = \frac{9}{x}\)
        
        https://drive.google.com/file/d/1uU9pOF7RVXt1H40x7T1U2hpF7pixjd6Q/view?usp=sharing This function shifts by making the lines move outward away from the (0,0) point.
    - - \(f(x)=x^2\)
        
        \(f(x)=7x^2\)
    - - \(f(x)= log(x) \)
        
        \( f(x)= log(x+3) \)
        
        https://drive.google.com/file/d/1z-mlbUgL1rutB-mFnYbBMshJf8D8s-4V/view?usp=sharing This function shifts to make the asymptote at -3 on the x-axis.
    - - \(f(x)=x\)
        
        \(f(x)=4x \)
    - - \(f(x) = (\sqrt{x})\)
        
        \( f(x) = (\sqrt{x-2})\)
        
        https://drive.google.com/file/d/1j5kT7juAuqPb_oZPC1BArI6DOusd-cXR/view?usp=sharing This function shifts 2 units to the left
  - - - \( f(x) = x^2 + 2 \)
        \( f(y + 3) = (y + 3)^2 + 2 \)
        \( f(y + 3) = y^2 + 9 + 2 \)
        \( f(y + 3) = y^2 + 11 \)
      - \( f(x) = x^2 + 2\)
        \( f(5) = 5^2 + 2\)
        \( f(5) = 25 + 2 \)
        \( f(5) = 27\)
      - \( f(x) = 7x + 3 \)
        \( f(2y) = 7(2y) + 3 \)
        \( f(2y) = 14 + 7y + 3 \)
        \( f(2y) = 7y + 17 \)
      - Find \(f(x)\) when \(x = 4\) \(f (x) = 4x - 23\) \( f(x) = 4(4) - 23\) \( f(x) = 16 - 23 \) \( f(x) = -7 \)
  - - - Domain
        
        Domain is x values and how far left or right the line runs
      - Range
        
        The range is how far the y-values extend past the vertex
      - Zeroes
        
        Zeroes are points on the line where they cross the x-axis
      - Intervals of increasing value
        
        The interval of increasing value is the point after the vertex that the point increases
      - Intervals of decreasing value
        
        The interval of decreasing value is the point after the vertex that the point decreases
      - Maximums
        
        The highest value on the x-axis that the line goes to
      - Minimums
        
        The lowest value on the x-axis that the line touches
      - Asymptotes
        
        Asymptotes are lines on the x or y axis that the functions do not cross
- - - - Graph