Answer:
See attached
Step-by-step explanation:
You want a graph of 8x -6y = 0 from two ordered pairs that satisfy the equation.
Intercepts
We can find the x- and y-intercepts by solving the equation with y=0 and x=0, respectively. Doing that, we find ...
x-intercept = 0
y-intercept = 0
This means the origin (0, 0) is one point on the line.
Point
The difference of the x- and y-terms is zero, so we can find other points by using multiples of the y-coefficient for x while using multiples of the x-coefficient for y. Using (x, y) = (3, 4) we have ...
8·3 -6·4 = 0 . . . . . . (3, 4) is a point on the line
Plot
Now, we have the points (0, 0) and (3, 4), so we can graph the line as shown in the attachment.
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Additional comment
The standard form of the equation has the common factor of 2 removed from the coefficients:
4x -3y = 0
This is the form that suggests the point (x, y) = (3, 4).
Writing the equation as a proportional relation, we have ...
[tex]y=\dfrac{4}{3}x[/tex]
This suggests that suitable integer values for x are those that are multiples of 3.
