a To sketch a line, we need to know at least two points through which the line passes. The first point, we can locate by marking the line's y-intercept.
To find a second point, we can use the line's slope. A slope of 3 means that it will increase by 3 on the vertical axis for every 1 unit we travel in the positive horizontal direction.
The line through these points, have a y-intercept of (0,2) and a slope of 3.
y=mx+b
In this equation, m is the line's slope and b is the y-intercept. We have m=3 and b=2. We can now write the equation of the line.
y=3x+2
c Let's first calculate the first four terms of the sequence.
|c|c|c|
n & 3n-1 & t(n)
1 & 3( 1)-1 & 2
2 & 3( 2)-1 & 5
3 & 3( 3)-1 & 8
4 & 3( 4)-1 & 11
Next, we will plot these points on one set of axes, and the line on the other.
d The main difference between a line and a sequence is that a sequence is only defined for discrete values while a line is continuous. In other words, the domain is limited in the following way.
Sequence:& {x | x= 1,2,3,4... }
Function:& {x | x=All real numbers }
Let's now look at their equations.
Sequence:& t(n)=3n-1
Function:& y=3x+2
In both equations, the independent variable is multiplied by 3. In that respect they are similar.
