graph the line with slope -1/3 passing through the point (1, 4)
Explain how you would graph the line containing a slope of –1/5 that goes through the point (1,–4).
Oh, you want me to graph a line? Well, I'm not much of an artist, but I'll give it a shot! Imagine a straight line that starts at the point (1, 4). Now, this line has a slope of -1/3, which means for every 3 units you go to the right, it goes down 1 unit.
So, let's start at the point (1, 4). If we go 3 units to the right, we'll end up at (4, 4 - 1). Then, if we go 3 more units to the right, we'll end up at (7, 4 - 2). And if we keep going in this fashion, we'll start forming a downwards slope.
Once you connect all these points, you should end up with a pretty straight line. Voila! But, uh, don't expect a masterpiece. I'm more of a jokester than an artist.
To graph the line with slope -1/3 passing through the point (1, 4), follow these steps:
Step 1: Plot the given point (1, 4) on the coordinate plane.
Step 2: Use the slope (-1/3) to find another point on the line.
To find another point, you can move down 1 unit and to the right 3 units from the given point since the slope is -1/3. Starting from (1, 4), move down 1 unit to get to the next y-coordinate and then move to the right 3 units to get to the next x-coordinate.
Starting from (1, 4):
Move down 1 unit: (1, 4) -> (1, 3)
Move right 3 units: (1, 3) -> (4, 3)
So, another point on the line is (4, 3).
Step 3: Draw a straight line passing through the two points.
Now, plot the two points (1, 4) and (4, 3) on the coordinate plane and draw a straight line passing through them. This line represents the graph of the equation with a slope of -1/3 passing through the point (1, 4).
To graph a line with a given slope and passing through a specific point, you can follow these steps:
1. Start by plotting the given point (1, 4) on a coordinate plane. This point will be on the line we need to graph.
2. Use the slope to determine other points on the line. The slope represents the ratio of vertical change (rise) to horizontal change (run).
Since the slope is -1/3, this means for every 3 units you move to the right (run), you move down by 1 unit (rise).
3. Starting from the given point (1, 4), you can use the slope to find the next point. Move 3 units to the right and 1 unit down. This will give you the point (4, 3).
4. Repeat this step if needed. Since a line extends infinitely in both directions, you can continue using the same ratio (slope) to find more points.
Now, move 3 units to the right from (4, 3) and 1 unit down to get the point (7, 2). You can repeat this process in the opposite direction as well, moving 3 units to the left and 1 unit up.
5. Connect all the points you have plotted. This will give you a straight line passing through the given point (1, 4).
Your graph should now show a line passing through the points (1, 4), (4, 3), (-2, 5), (7, 2), and so on.
Note: Ensure that your scale is consistent and that you have enough points plotted to visualize the trend of the line accurately.
plot the point (1,4)
move down 1 and right 3. (slope = -1/3) Plot that point
Draw the line through the two points.