Question

choose the best graph that represents the linear equation: -2y = x + 6 graph a graph of a line on a coordinate plane graph b graph of a line on a coordinate plane save and exit

Explanation:

Step1: Rewrite the equation

First, rewrite the given linear equation \(-2y = x + 6\) in slope - intercept form (\(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept). Divide both sides of the equation by \(- 2\):

$$y=-\frac{1}{2}x - 3$$

The slope \(m =-\frac{1}{2}\) (negative, so the line should be decreasing from left to right) and the y - intercept \(b=-3\) (the line crosses the y - axis at \((0,-3)\)).

Step2: Analyze Graph A

In Graph A, the line crosses the y - axis at \((0, - 3)\) (matches the y - intercept of our equation) and has a negative slope (the line is going down as we move from left to right, which matches the slope \(m =-\frac{1}{2}\)).

Step3: Analyze Graph B

Graph B has a positive slope (the line is going up as we move from left to right) and its y - intercept does not appear to be \(-3\), so it does not match the equation \(y =-\frac{1}{2}x-3\).

Answer:

Graph A