**Unit 2 Overview – Linear Equation**

? write recursive routines emphasizing start plus change

? study rate of change (SLOPE)

? learn to write equations for lines using a starting value (y-intercept) and a rate of change (SLOPE)

? use equations and tables to graph lines

? solve linear equations

A **recursive sequence** is an ordered list of numbers defined by a starting value and a rule. You generate the sequence by applying the rule to the starting value, then applying it to the resulting value, and repeating this process.

Real World Application –

The Empire State Building in New York City has 102 floors and is 1250 ft high. How high up are you when you reach the 80th floor? You can answer this question using a recursive sequence. The starting value is -4 because the basement is 4 ft below ground level.

Solution – Each floor is 13 ft higher than the floor below it, so the rule for finding the next floor height is “add 13 to the current floor height.”

**Linear Equation**

y = mx+b – is the intercept form. The value of a is the y-intercept, which is the value of y when x is zero. The intercept gives the location where the graph crosses the y-axis. The number multiplied by x is b, which is called the coefficient of x.

Real World Application –

In the equation y = 215 + 3.8x, 215 is the value of a. It represents the 215 calories Manisha burned while jogging before her workout. The value of b is 3.8. It represents the rate her body burned calories while she was pedaling. What would happen if Manisha chose a different physical activity before pedaling on the stationary bike?