- Linear equations are polynomials of order 1 and can be written in various ways depending on needs
- Slope intercept: \(y=mx+b\)… \(y=3x+4\); \(y=-\Large \frac{2}{3x}\normalsize -\sqrt{5}\)
- Standard form; \(ax+by=c\)… \(x+2y=7\); \(2x-4y=0\)
- Point-slope: \(y-y_1=m(x-x_1)\)… \(y-4=6(x+3)\); \(y+3=-2(x-\pi)\)
- \(y=m(x-h)+k\) (transformation form)… \(y=4(x-7)-3\)
- All lines are functions except those that represent a vertical line, \(x=b\)… \(x=4\)
Slope is the rate of change of a linear function and is a measure of the steepness of a line. Slope is often designated with an m.
- Slope is the ratio of the change in \(y\) per change in \(x\):
\[m=\frac{\Delta y}{\Delta x} \\ m=\frac {rise}{run}\]
- On a graph, it can be helpful to draw slope triangles.
- Given two points on the line, \((x_1,\,y_1)\) and \((x_2,\,y_2)\), \[m=\frac{(y_2-y_1)}{(x_2-x_1)}\]
\[m=\frac{1}{2}\]