These are still being edited!!!
Here is a supplement to the textbook which covers everything about lines that we need to know:
Important information about lines and linear equations: (And equations in general)
A solution to an equation in two variables is an ordered pair (a point in the coordinate plane) which satisfies that equation.
The graph of any equation is a picture of the set of all solutions to that equation.
A linear equation is an equation in which all variables are to the first power (and no term contains more than one variable).
The graph of a linear equation in two variables is a line.
Note: “line” in mathematics always means a straight line.
The slope of a line in the plane measures how “tilted” that line is. Another way to say this: the slope gives the direction of the line. It represents the rate of change of the y-values.
Definition: given any two points on a line, $A = (x_A, y_A)$ and $B = (x_B, y_B)$, the slope of the line is defined as $m = \frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x} = \frac{y_A – y_B}{x_A – x_B}$
Three important forms of the equation of a line:
Slope-intercept form – the most important, usually
$y = mx + b$
where $m$ is the slope of the line and $b$ is the y-intercept.
Either $m$ or $b$ or both may be 0.
“Standard” form
Ax + By + C = 0
Point-slope form: if $(x_A, y_A)$ is a point on the line
$y – y_A = m(x – x_A)$
Parallel lines have the same slopes.
Perpendicular lines are lies which intersect in a right angle. Their slopes are negative reciprocals: if one of the slopes is $\frac{a}{b}$, the other slope is $-\frac{b}{a}$.
Another way to say this: the product of the two slopes is-1.
