\( P ( - 4 , - 5 ) , y = 6 x - 7 \)

Did you know that the point \( P(-4, -5) \) can be tested for whether it lies on the line represented by the equation \( y = 6x - 7 \)? To check, we can substitute \( x = -4 \) into the equation and see if the resulting \( y \) value matches -5. Doing the math, we find \( y = 6(-4) - 7 = -24 - 7 = -31 \), which means \( P \) does not lie on the line! Now, if you're looking to find the distance from point \( P \) to the line \( y = 6x - 7 \), you can use the point-to-line distance formula! That’s right, this little gem calculates the shortest distance to a line without having to plot anything. Just plug in the values for \( x_0, y_0 \) of point \( P \) into the formula and voilà! You'll always have a lovely answer, showcasing your math prowess!