You can see the line represented on the graph for the equation y= -x+1 in the image attached below.
To graph the line represented by the equation y = -x + 1, we can follow a few steps:
1. First, let's understand the equation. In this case, we have y = -x + 1. The equation is in slope-intercept form, which means it is written as y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
2. From the equation, we can determine that the slope of the line is -1 (since the coefficient of x is -1). This means that for every unit increase in x, y decreases by 1 unit.
3. Next, let's locate the y-intercept. The y-intercept is the value of y when x = 0. In this case, when x = 0, we have y = -0 + 1 = 1. So, the y-intercept is the point (0, 1).
4. Now, let's plot the y-intercept on the graph. Place a point at the coordinates (0, 1).
5. To find additional points on the line, we can use the slope. Starting from the y-intercept, we can move one unit to the right (positive x) and one unit downward (negative y) to get the next point. This gives us the coordinates (1, 0).
6. Now, we can connect the two points on the graph using a straight line. The line represents the equation y = -x + 1.
Remember to label the axes and add any additional markings to make the graph clear and understandable.