Chapters 4      Linear Equations and Inequalities in two variables

1. Rectangular coordinate system- ordered pairs (x, y)

    Each point on the plane represents a unique ordered pair

2.  Linear equations in two variables- when graphed they give a line

     Standard form           Ax + By = C , where A, B, and C are constants

     Slope-intercept form   y = mx + b;  m is the slope and b is the y-intercept

     Point-slope form   y - y₁ = m (x - x₁) ; line passes through ( x₁, y₁), m is its slope 

    Slope of line = rise/run =  change in y/change in x =  (y₂ - y₁)/(x₂ - x₁)

3. Function- how is it different from a relation?

   Relation is a set of ordered pairs (x, y). A function is a relation in which for each value of x in the domain gives a unique value in the range.

Notation  y = f(x), if  f(x) = mx + b  it represents a linear function

4. Graphing linear equations and inequalities

5. Variation

    Direct variation-   y varies directly with x means that y = kx where k is a constant; example- when a car is moving at steady speed, the distance traveled by the car varies directly with the travel time. As x increases y will increase in the same proportion.

    Inverse variation- y varies inversely with x means that y = k/x where k is a constant, example- at a given temperature the pressure of an enclosed gas varies inversely with volume. As x increases y will decrease and vice-versa.