Answer:
To plot the line for the equation y - 2 = -2(x + 4), we can first rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Let's start by simplifying the given equation:
y - 2 = -2(x + 4)
y - 2 = -2x - 8
Next, let's isolate y by adding 2 to both sides:
y = -2x - 6
Now we have the equation in slope-intercept form. We can identify the slope and y-intercept from this equation:
The slope (m) is -2, and the y-intercept (b) is -6.
To plot the line, we can start by plotting the y-intercept, which is the point (0, -6). This point represents where the line crosses the y-axis.
Next, we can use the slope to find additional points on the line. The slope of -2 means that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 2. So, we can choose another point by moving 1 unit to the right and 2 units down from the y-intercept. This gives us the point (1, -8).
By connecting the plotted points (0, -6) and (1, -8) with a straight line, we have the graph of the equation y - 2 = -2(x + 4).