Linear Relations 2

Question

x y
1 4
3 14
5 24
7 34
9 44

x goes up by +2 each time.
y goes up by +10 each time.

For this linear relation, develop the equation for the relation

Answer 1

The slope-intercept form of the equation of a line looks like:   y=mx+b

     where m=slope=(change in y-values)/(change in x-values)   and the point (0,b) is the y-intercept (where x=0)

 

The point-slope form of the equation of a line is:

    (y-y₁) = m(x-x₁)     where m=slope=(y₂-y₁)/(x₂-x₁) often called "rise over run"

 

For this problem, "x goes up by +2 each time" and "y goes up by +10 each time" means slope=m=(+10)/(+2)

 

Now, put any point [they are in the form of {x,y) into the point-slope form of the equation and solve for y.  That gives you the equation in slope-intercept form.  For example:

     y = ((+10/(+2))(x) + b

     4 = 5(1) + b

     -1 = b

 

The equation for this line is:  y=5x - 1