Questions: For the equation y-3=2(x+4) it has a slope of 2 and contains what

Solution Steps

To find if the point \((-3, -4)\) lies on the line given by the equation \(y - 3 = 2(x + 4)\), we need to substitute the \(x\) and \(y\) values of the point into the equation and check if the equation holds true. If it does, the point lies on the line; otherwise, it does not.

We start with the equation of the line given by:

\[ y - 3 = 2(x + 4) \]

We will substitute the point \((-3, -4)\) into the equation. Here, \(x = -3\) and \(y = -4\).

Substituting \(x = -3\) into the equation:

\[ y - 3 = 2(-3 + 4) \]

Calculating the right side:

\[ y - 3 = 2(1) = 2 \]

Now, we can solve for \(y\):

\[ y - 3 = 2 \implies y = 2 + 3 = 5 \]

The calculated \(y\) value is \(5\), while the given \(y\) value from the point is \(-4\). Since \(5 \neq -4\), the point does not lie on the line.

Final Answer