Graph the line through the point
1, 1
having slope
−4/5
. Then give
2
other points on the line.
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Graph the line through the point
1, 1
having the slope
−4/5
.
To graph the line through the point (1, 1) with a slope of -4/5, we can use the point-slope form equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Substituting the values into the equation, we have:
y - 1 = (-4/5)(x - 1)
Simplifying the equation:
y - 1 = (-4/5)x + 4/5
Now we can rewrite the equation in slope-intercept form (y = mx + b):
y = (-4/5)x + 9/5
Now we can graph the line by plotting the given point (1, 1) and finding two more points on the line:
By setting x = 0, we get:
y = (-4/5)(0) + 9/5
y = 9/5
So another point on the line is (0, 9/5).
By setting x = 5, we get:
y = (-4/5)(5) + 9/5
y = -4 + 9/5
y = 1/5
So another point on the line is (5, 1/5).
Now we can plot the three points (1, 1), (0, 9/5), and (5, 1/5) on a graph and draw a line through them.
Here is the graph of the line through the point (1, 1) with a slope of -4/5:
```
(0, 9/5)----(1, 1)----(5, 1/5)
```
Note: The graph of the line may not be perfectly accurate as I am unable to draw it with exact precision.
To graph the line through the point (1,1) with a slope of -4/5, we can use the point-slope form of a linear equation.
The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Given that the point is (1,1) and the slope is -4/5, we can substitute these values into the point-slope form to get the equation:
y - 1 = (-4/5)(x - 1)
Now, let's simplify the equation:
y - 1 = (-4/5)x + 4/5
Next, we can rewrite this equation in slope-intercept form (y = mx + b) by isolating y:
y = (-4/5)x + 4/5 + 1
y = (-4/5)x + 9/5
Now that we have the equation in slope-intercept form, we can graph the line.
Choose any x-values and substitute them into the equation to find the corresponding y-values. Let's choose x = 0 and x = 2.
For x = 0:
y = (-4/5)(0) + 9/5
y = 9/5
So the first point is (0, 9/5).
For x = 2:
y = (-4/5)(2) + 9/5
y = -8/5 + 9/5
y = 1/5
So the second point is (2, 1/5).
Now we can plot these three points on a graph and draw a line through them.
To graph the line through the point (1, 1) with a slope of -4/5, you can follow these steps:
1. Plot the given point (1, 1) on the coordinate plane. This point represents one point on the line.
2. Use the slope to determine the direction and steepness of the line. Since the slope is -4/5, it means that for every 4 units you move down the y-axis, you move 5 units to the right on the x-axis.
3. Starting from the given point (1, 1), move 5 units to the right and then 4 units down. This will give you the coordinates of the second point on the line.
4. Repeat step 3 to find the coordinates of the third point. Move 5 units to the right from the second point and then 4 units down.
Now you have three points on the line. You can connect these points to graph the line.