Ahistorian would most likely interpret the rhetoric in the passage as evidence that

1. 2x + 3y = 1470
    3y = -2x + 1470
    y = -2/3x + 490 <== slope intercept form

2. y = -2/3x + 490slope = -2/3y int = (0,490)
    to graph, start at (0,490)since the slope is -2/3, we will go down 2       spaces, then to the right 3 spaces, then down 2 spaces, and to the right 3 spaces. It helps to find the x int which can be found by subbing in 0 for y into the equation and finding x. So ur x int is (735,0)...this is where ur line should cross the x axis.

3. function notation : f(x) = -2/3x + 490...not sure how to explain the meaning...sorry

4. graph the functionit will be the same line as the graph I explained before...y = -2/3x + 490
y int = (0,490)
x int = (735,0)

5. original :                            new :
    2x + 3y = 1470                 2x + 3y = 1593
    3y = -2x + 1470                3y = -2x + 1593
     y = -2/3x + 490                y = -2/3x + 531

similarities : Both of these equations will have the same slope, which is -2/3. Both lines are descending. Both lines are parallel to each other.

differences : These lines will have different x and y intercepts
y = -2/3x + 490 : y int = (0,490), x int = (735,0)
y = -2/3x + 531 : y int = (0,531), x int = (796.5,0)

6. pick 2 points on the line(0,300) and (450,0)
find the slope using the slope formula : slope = (y2 - y1) / (x2 - x1)
(0,300)x1 = 0 and y1 = 300
(450,0)...x2 = 450 and y2 = 0
now we sub and find the slope
slope = (0 - 300) / (450 - 0) = -300/450 reduces to -2/3

now we use y = mx + b
slope(m) = -2/3
use either of ur points...(450,0)...x = 450 and y = 0
now sub and find b, the y int
0 = -2/3(450) + b
0 = - 300 + b
300 = b

so ur equation is : y = -2/3x + 300or  2x + 3y = 900