Questions: (-2,3), y=-1/2 x-4

Transcript text: $(-2,3), y=-\frac{1}{2} x-4$

Solution

Step 1: Identify the Problem

We are given a point $(-2, 3)$ and a line equation $y = -\frac{1}{2}x - 4$. The task is to determine if the point lies on the line.

Step 2: Substitute the Point into the Line Equation

To check if the point $(-2, 3)$ lies on the line, substitute $x = -2$ and $y = 3$ into the line equation:

\[ y = -\frac{1}{2}x - 4 \]

Substitute $x = -2$:

\[ y = -\frac{1}{2}(-2) - 4 \]

Calculate the right-hand side:

\[ y = 1 - 4 = -3 \]

Step 3: Compare the Calculated and Given $y$-Values

The calculated $y$-value is $-3$, while the given $y$-value is $3$. Since these values are not equal, the point $(-2, 3)$ does not lie on the line.

The point $(-2, 3)$ does not lie on the line $y = -\frac{1}{2}x - 4$.

\[ \boxed{\text{The point does not lie on the line.}} \]

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