The graph of y = -x + 1 is a straight line with a slope of -1 and a y-intercept at (0, 1). Key points include the y-intercept (0, 1), (1, 0), and another point (2, -1).
To graph the equation y + 2 = -(x - 3), let's first rewrite it in slope-intercept form (y = mx + b):
y + 2 = -(x - 3)
Distribute the negative sign:
y + 2 = -x + 3
Subtract 2 from both sides:
y = -x + 1
Now, the equation is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
**Slope:** The coefficient of x is -1, so the slope (m) is -1.
**Y-Intercept:** The y-intercept (b) is 1.
Now, let's plot the graph using the slope and y-intercept.
**Graph:**
1. Plot the y-intercept at the point (0, 1).
2. Use the slope to find another point. The slope is -1, so from the y-intercept, move down 1 unit and to the right 1 unit to get another point (1, 0).
3. Choose another point. For example, let x = 2. Substitute into the equation to find y:
y = -x + 1
y = -2 + 1
y = -1
So, another point is (2, -1).
Now, plot these points and draw the line. The graph should show a straight line with a slope of -1 and a y-intercept at (0, 1).