derive the equation of the line in slope-intercept form.
the coordinates are (1, -1) and (0, -4) and the line passe through the one on the x axis.
To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope, denoted as "m," is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates (1, -1) and (0, -4):
m = (-4 - (-1)) / (0 - 1)
m = (-4 + 1) / (-1)
m = -3 / (-1)
m = 3
Now that we have the slope, we can use the point-slope form of a line, which is:
y - y₁ = m(x - x₁)
Using the point (1, -1):
y - (-1) = 3(x - 1)
y + 1 = 3(x - 1)
Next, we simplify this equation:
y + 1 = 3x - 3
y = 3x - 4
Therefore, the equation of the line in slope-intercept form is y = 3x - 4.
write the equation of the line in slope-intercept form. the coordinates are (0, 1) and (1, -4) and the line passes through the 1 on the y-axis.
To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope, denoted as "m," is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates (0, 1) and (1, -4):
m = (-4 - 1) / (1 - 0)
m = (-4 - 1) / 1
m = -5 / 1
m = -5
Now, we need to find the y-intercept, which is the point where the line crosses the y-axis. Since the line passes through the point (1, -1) on the y-axis, the y-intercept is -1.
Using the slope-intercept form of a line, which is y = mx + b (where m is the slope and b is the y-intercept):
y = -5x - 1
Therefore, the equation of the line in slope-intercept form is y = -5x - 1.
r u sure?
Apologies for the previous response. I made an error in my calculations. Let's go through it again correctly.
To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope, denoted as "m," is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates (0, 1) and (1, -4):
m = (-4 - 1) / (1 - 0)
m = (-4 - 1) / 1
m = -5 / 1
m = -5
Now, we need to find the y-intercept, which is the point where the line crosses the y-axis. Since the line passes through the point (0, 1) on the y-axis, the y-intercept is 1.
Using the slope-intercept form of a line, which is y = mx + b (where m is the slope and b is the y-intercept):
y = -5x + 1
Therefore, the equation of the line in slope-intercept form is y = -5x + 1.
graph the linear equation y= -3x+2
To graph the linear equation y = -3x + 2, we can start by plotting a few points and then connect them to create the line.
First, let's choose some x-values and find the corresponding y-values using the equation.
When x = 0:
y = -3(0) + 2
y = 2
So, when x = 0, y = 2. This gives us the point (0, 2).
When x = 1:
y = -3(1) + 2
y = -3 + 2
y = -1
So, when x = 1, y = -1. This gives us the point (1, -1).
When x = -1:
y = -3(-1) + 2
y = 3 + 2
y = 5
So, when x = -1, y = 5. This gives us the point (-1, 5).
Now, we can plot these points on a graph and connect them to draw the line.
Here is the graph of the linear equation y = -3x + 2:
```
|
6 | .
| .
5 | .
| .
4 |
|
3 |
|
2 | .
| .
1 | .
|.
0 +-------------------------
-2 -1 0 1 2 3 4 5
```
The line passes through the point (0, 2) on the y-axis and has a slope of -3. It has a downward slope, meaning it goes from left to right.