Notes for Chapter 5 exam.

This is all that Miles needs to know to do well on his chapter 5 exam. Equation 1. Calculating slope. Equation 2. Point slope form. Remember that  is calculated using equation 1. Equation 3. Slope intercept form. Remember that  is calculated using equation 1.  Also if you are only give two points you can first calculate  using equation 1, then use equation 2 to put it in point slope form, then solve for . Graphing an equation in slope intercept from means plotting point  then taking the fraction  and moving up or down based on the numerator and right based on the denominator. Equation 4. Standard form.  Where a, b and c are constants.  Just get everything on the left side of the equation except 0.

Graph of line.

Below is the graph of .  Note that the point A is the y-intercept.  You get to point B by going up 3 and over 2.

Graph of line

Parallel lines.

Find a parallel line by adding a constant to  for a line in  form. For example: If you have a line  then  and  are both parallel

Perpendicular lines

Find perpendicular lines by taking the opposite reciprocal of .  The opposite reciprocal of a fraction means you negate the fraction and flip it.  For a whole number put 1 over the number. Examples: The opposite reciprocal of 1/3 = -3.  The opposite reciprocal of -2/3 = 3/2. To find a perpendicular line to  take the opposite reciprocal of 3/2 and get

Translating absolute value graphs.

To translate an absolute value graph up or down, add or subtract a constant outside the absolute value. For  translate up 2 by using   and translate down 2 by using . To translate an absolute value graph right or left, subtract (for right) or add (for left) a constant inside the absolute value. For  translate right 2 by using  and translate right 2 by using . You can translate up or down and left or right simultaneously.   translates right 2 and up 3.