Answer:
The error is in computing the y intercept. It should be at (0, -6) not (0, 6)
Step-by-step explanation:
The equation of the line is
[tex]-\frac{3}{4} x - 6[/tex]
y intercept is at point x = 0
When x = 0,
[tex]y = -\frac{3}{4} x - 6\\\\y = 0 - 6 \\\\y = -6[/tex]
So y intercept is at point (0, -6)
If we plot a second point 3 units down and 4 units right we should get the point 0 + 4, -6 - 3) = (4, -9)
Plugging this into the original correct equation satisfies the equation
[tex]y = -\frac{3}{4} x - 6\\\\y = -\frac{3}{4} (4) - 6 \\\\y = -3 -6 = -9 \\\\[/tex]
So we can see that the line does pass through (4, -9)
See attached graph for further clarification
