Graph the line with slope 1/3 passing through the point (2, - 5).
To graph the line with slope 1/3 passing through the point (2, -5), we can use the point-slope form of a line:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is a point on the line. Substituting m = 1/3, x1 = 2, and y1 = -5, we get:
y - (-5) = (1/3)(x - 2)
Simplifying and rearranging, we get the slope-intercept form of the line:
y = (1/3)x - (11/3)
Now we can plot the point (2, -5) and use the slope to find another point on the line. The slope of 1/3 means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 1/3. So we can add 3 to the x-coordinate of the point (2, -5) to get a new point with y-coordinate -4:
(2, -5) --> (5, -4)
Plotting these two points and connecting them with a straight line gives us the graph of the line with slope 1/3 passing through the point (2, -5):
To graph a line with a given slope and passing through a given point, you can follow these steps:
Step 1: Plot the given point (2, -5) on a coordinate plane.
Step 2: Use the slope to find another point on the line. Since the slope is 1/3, this means that for every 1 unit we move to the right, we go up by 1/3 units.
Starting from the point (2, -5), we can move 3 units to the right and 1 unit up to find another point.
So, starting from (2, -5), we have:
Move 3 units to the right: (2 + 3, -5) = (5, -5)
Move 1 unit up: (5, -5 + 1) = (5, -4)
So, another point on the line is (5, -4).
Step 3: Connect the two points (2, -5) and (5, -4) to draw the line.
The graph of the line with slope 1/3 passing through the point (2, -5) looks like this:
```
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____|____|____|____|____|____|____|____|____
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(2, -5) (5, -4)
```
Note: The horizontal lines represent the x-axis, and the vertical lines represent the y-axis.