Answer:
To graph the line with slope 1 passing through the point (3,-1), we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
Substituting m = 1, x1 = 3, and y1 = -1, we get:
y - (-1) = 1(x - 3)
Simplifying this equation, we get:
y + 1 = x - 3
Subtracting 1 from both sides, we get:
y = x - 4
So the equation of the line is y = x - 4. To graph this line, we can plot the point (3, -1) and use the slope of 1 to find additional points. For example, we can go up 1 unit and right 1 unit from the point (3, -1) to get the point (4, 0). We can then connect these two points to graph the line:
|
4 | ●
3 |
2 |
1 |
0 | ●
|________
1 2 3
The line passes through the points (3, -1) and (4, 0), and continues infinitely in both directions.