This is all that Miles needs to know to do well on his chapter 5 exam.[br][br]Equation 1. Calculating slope.[br][br][math]m=\frac{\left(y2-y1\right)}{\left(x2-x1\right)}[/math][br][br]Equation 2. Point slope form.[br][math]y-y_1=m\left(x-x_1\right)[/math][br]Remember that [math]m[/math] is calculated using equation 1.[br][br]Equation 3. Slope intercept form.[br][math]y=mx+b[/math][br]Remember that [math]m[/math] is calculated using equation 1.  Also if you are only give two points you can first calculate [math]m[/math] using equation 1, then use equation 2 to put it in point slope form, then solve for [math]y[/math].[br][br]Graphing an equation in slope intercept from means plotting point [math]\left(0,b\right)[/math] then taking the fraction [math]m[/math] and moving up or down based on the numerator and right based on the denominator.[br][br]Equation 4. Standard form.[br][math]ax+by+c=0[/math] Where a, b and c are constants.  Just get everything on the left side of the equation except 0.

Below is the graph of [math]y=\frac{3}{2}x+2[/math].  Note that the point A is the y-intercept.  You get to point B by going up 3 and over 2.

Find a parallel line by adding a constant to [math]b[/math] for a line in [math]y=mx+b[/math] form.[br][br]For example: If you have a line [math]y=\frac{3}{2}x+2[/math] then [math]y=\frac{3}{2}x+4[/math] and [math]y=\frac{3}{2}x-3[/math] are both parallel

Find perpendicular lines by taking the opposite reciprocal of [math]m[/math].  The opposite reciprocal of a fraction means you negate the fraction and flip it.  For a whole number put 1 over the number.[br][br]Examples: The opposite reciprocal of 1/3 = -3.  The opposite reciprocal of -2/3 = 3/2.[br][br]To find a perpendicular line to [math]y=\frac{3}{2}x+2[/math] take the opposite reciprocal of 3/2 and get [math]y=-\frac{2}{3}x+2[/math]

To translate an absolute value graph up or down, add or subtract a constant outside the absolute value.[br][br]For [math]y=|x|[/math] translate up 2 by using  [math]y=|x|+2[/math] and translate down 2 by using [math]y=|x|-2[/math] .[br][br]To translate an absolute value graph right or left, subtract (for right) or add (for left) a constant [i]inside[/i] the absolute value.[br][br]For [math]y=\left|x\right|[/math] translate right 2 by using [math]y=\left|x-2\right|[/math] and translate right 2 by using [math]y=\left|x+2\right|[/math].[br][br]You can translate up or down and left or right simultaneously.  [math]y=\left|x-2\right|+3[/math] translates right 2 and up 3.[br]