Answer:
Explanation:
every time x goes up 1, y goes up 4
x = 3 minus x = 2 is a delta (a change of 1)
x = 4 minus x = 3 is a delta (a change of 1)
x = 5 minus x = 4 is a delta (a change of 1)
the delta x is ALWAYS 1 for this table you can always substract x's to find the delta delta is symbolized by Δ Δx for the delta x
y = 7 minus y = 3 is a delta (a change of 4)
y = 11 minus y = 7 is a delta (a change of 4)
y = 15 minus y = 11 is a delta (a change of 4)
the delta y is ALWAYS 4 for this table you can always substract y's to find the delta delta is symbolized by Δ Δy for the delta y
the slope m = Δy / Δx m = 4 / 1 m = 4
y = mx + b when x = 0 then y = b (called the y intercept)
so how do we find the y intercept?
look at the pattern in the TABLE Δx and Δy
when x = 1 y = (3 - 4) = -1
x = 0 y =( -1 - 4) = -5
so y = 4x - 5 is a line equation for the data in this table
I believe there are other forms for linear equations
I chose the y-intercept form
use the point slope equation
(y - y1) = m(x - x1) where (x1, y1) are the coordinates of a point on
the line
when you know the slope of the line and a point on the line
as before
m = (y2 - y1) / (x2 - x1) from the table
= (7 - 3) / (3 - 2) still equals
= 4/1 = 4
pick a point on the line say x= 4 and y = 11 (4, 11)
(y - y1) = m(x - x1)
y - 11 = 4(x - 4) point slope form
solving point slope form for y
y - 11 = 4x - 16 add 11 to both sides
y = 4x - 5 back to the y-intercept form