6. Graph $$ y=-\frac{2}{3} x+1 $$. Is point $$ (-6,4) $$ a solution?

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UpStudy AI · Accepted Answer

1. **Write the equation:**  
   The equation of the line is  
   $$
   y = -\frac{2}{3}x + 1.
   $$

2. **Test the given point $$(-6, 4)$$:**  
   Substitute $$ x = -6 $$ into the equation to see if the resulting $$ y $$ equals $$ 4 $$.
   $$
   y = -\frac{2}{3}(-6) + 1.
   $$

3. **Simplify the expression:**  
   First calculate $$-\frac{2}{3}(-6)$$:
   $$
   -\frac{2}{3}(-6) = \frac{12}{3} = 4.
   $$  
   Then add $$ 1 $$:
   $$
   y = 4 + 1 = 5.
   $$

4. **Compare the result with the given point:**  
   The computed $$ y $$-coordinate is $$ 5 $$ while the given point has $$ y = 4 $$. Therefore,
   $$
   5 \neq 4.
   $$

5. **Conclusion:**  
   Since the computed $$ y $$-value does not match the $$ y $$-coordinate of the given point, the point $$(-6, 4)$$ is not a solution to the equation.
The point $$(-6, 4)$$ is not a solution to the equation $$ y = -\frac{2}{3}x + 1 $$.

6. Graph \( y=-\frac{2}{3} x+1 \). Is point \( (-6,4) \) a solution?

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