LINR 2 | Lesson 2 | (extras)

• 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 $$(x_2,\,y_2)$$, $m=\frac{(y_2-y_1)}{(x_2-x_1)}$

$m=\frac{1}{2}$