Question

on a piece of paper, graph $y = -3x - 2$. then determine which answer matches the graph you drew.
a. image of a graph with a red line and two red dots, labeled (1,1) and another point on the y-axis

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=-3x - 2\), the slope \(m=-3\) and the y - intercept \(b = - 2\).

Step2: Analyze the y - intercept

The y - intercept is the point where \(x = 0\). Substituting \(x = 0\) into \(y=-3x - 2\), we get \(y=-3(0)-2=-2\). So the line should cross the y - axis at \((0,-2)\).

Step3: Analyze the slope

The slope \(m=-3\), which means for every 1 unit we move to the right along the x - axis, we move down 3 units along the y - axis (or for every 1 unit left, we move up 3 units).

Step4: Evaluate Option A

In Option A, the y - intercept shown is not \((0, - 2)\) (it seems to be around \((0,-1)\) or something else) and the slope - based movement also does not match (the line in A has a positive slope, but our line has a negative slope). Wait, maybe the user's image has more options, but based on the equation \(y=-3x - 2\), let's re - check. The slope is negative, so the line should be decreasing from left to right. The y - intercept is at \((0,-2)\). If we plug in \(x = 1\), \(y=-3(1)-2=-5\), not 1. So Option A is incorrect. But since the problem is about graphing a linear equation, we can find the correct graph by using the y - intercept \((0,-2)\) and the slope of - 3.

Answer:

To determine the correct graph of \(y=-3x - 2\):

1. Y - intercept: When \(x = 0\), \(y=-3(0)-2=-2\), so the line passes through \((0,-2)\).
2. Slope: The slope \(m=-3\) (a negative slope, so the line decreases from left to right). For every \(x\) increase of 1, \(y\) decreases by 3. For example, when \(x = 1\), \(y=-3(1)-2=-5\); when \(x=-1\), \(y=-3(-1)-2 = 1\).

If we assume that the correct graph (not fully shown in the provided image) will have a y - intercept at \((0,-2)\) and a negative slope (decreasing line), we can eliminate Option A (since it has a positive slope and incorrect y - intercept and point \((1,1)\) which does not satisfy \(y=-3x - 2\) as \(y=-5\) when \(x = 1\)).

(Note: If more options were provided, we would check which one has the y - intercept \((0,-2)\) and a negative slope. For now, based on the equation, the correct graph will be the one with \(y\) - intercept \((0,-2)\) and a negative slope.)