The general form and the standard form of the graph equation are 13x - 8y = 17 and 13x - 8y - 17 = 0 respectively
How to determine the equations?
From the graph, we have the following points
(x,y) = (5,6) and (-3,-7)
Start by calculating the slope:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
This gives
[tex]m = \frac{-7 - 6}{-3 - 5}[/tex]
Evaluate the differences
[tex]m = \frac{-13}{-8}[/tex]
Evaluate the quotient
[tex]m = \frac{13}{8}[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
This gives
[tex]y = \frac{13}8(x - 5) + 6[/tex]
Multiply through by 8
8y = 13(x - 5) + 48
Open the bracket
8y = 13x - 65 + 48
Evaluate the like terms
8y = 13x - 17
Subtract 13x from both sides
-13x + 8y = -17
Multiply through by -1
13x - 8y = 17 ---- this represents the standard form
Subtract 17 from both sides
13x - 8y - 17 = 0 --- this represents the general form
Hence, the general form and the standard form of the graph equation are 13x - 8y = 17 and 13x - 8y - 17 = 0 respectively
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