6. Graph \( y=-\frac{2}{3} x+1 \). Is point \( (-6,4) \) a solution?
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To check if point \((-6, 4)\) is a solution of the equation \(y = -\frac{2}{3}x + 1\), we can substitute \(x = -6\) into the equation: \[ y = -\frac{2}{3}(-6) + 1 = \frac{12}{3} + 1 = 4 + 1 = 5. \] Since the calculated \(y\)-value is 5 and not 4, point \((-6, 4)\) is not a solution to the equation. Now, about graphing: Start by plotting the y-intercept at (0, 1). From there, use the slope of \(-\frac{2}{3}\) to move down 2 units and right 3 units to mark another point. Connect the dots, and voilà! You've got a line!