Question

graph the line.
$y = -2x - 4$

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 \(y=-2x - 4\), the slope \(m=-2\) and the y - intercept \(b = - 4\). This means the line crosses the y - axis at \((0,-4)\).

Step2: Find another point using the slope

The slope \(m=-2=\frac{-2}{1}\), which means for every 1 unit we move to the right (increase in \(x\) by 1), we move down 2 units (decrease in \(y\) by 2). Starting from the y - intercept \((0,-4)\), if we move \(x = 1\), then \(y=-2(1)-4=-6\), but we can also use the slope to find a point from the y - intercept in the other direction. If we move \(x=-2\) (2 units to the left), then \(y=-2(-2)-4 = 4 - 4=0\), so the point \((-2,0)\) is also on the line.

Step3: Check the graph

The graph shows a line passing through \((0,-4)\) (the y - intercept) and \((-2,0)\), which matches the points we found using the equation \(y = - 2x-4\). The slope of the line in the graph is also consistent with a slope of - 2 (as the line is decreasing from left to right, and the rise over run between \((-2,0)\) and \((0,-4)\) is \(\frac{-4 - 0}{0-(-2)}=\frac{-4}{2}=-2\)).

Answer:

The graph of \(y = - 2x-4\) is correctly drawn as it passes through the points \((0,-4)\) (y - intercept) and \((-2,0)\) (found using the slope - intercept form and slope calculation), and the slope of the line in the graph is - 2, which matches the equation.