Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To graph the line given by the equation [tex]\( y = 2x - 6 \)[/tex], follow these steps:
1. Identify the Equation and Components:
- The given equation is [tex]\( y = 2x - 6 \)[/tex].
- The equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where:
- [tex]\( m \)[/tex] is the slope (rate of change) of the line.
- [tex]\( b \)[/tex] is the y-intercept (the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]).
2. Determine the Slope and Y-Intercept:
- [tex]\( m = 2 \)[/tex] (slope), which means that for every unit increase in [tex]\( x \)[/tex], [tex]\( y \)[/tex] increases by 2 units.
- [tex]\( b = -6 \)[/tex] (y-intercept), which means the line crosses the y-axis at [tex]\( y = -6 \)[/tex].
3. Plot the Y-Intercept:
- Locate the point [tex]\( (0, -6) \)[/tex] on the graph and put a point there. This is the y-intercept.
4. Use the Slope to Find Another Point:
- Starting from the y-intercept [tex]\( (0, -6) \)[/tex], use the slope [tex]\( m = 2 \)[/tex] to find another point.
- Since the slope is [tex]\( 2 \)[/tex], move up 2 units in the y-direction and 1 unit in the x-direction.
- Doing this, from [tex]\( (0, -6) \)[/tex], we move to the point [tex]\( (1, -4) \)[/tex].
5. Plot the Second Point:
- Locate the point [tex]\( (1, -4) \)[/tex] on the graph and put a point there.
6. Draw the Line:
- Draw a straight line passing through the points [tex]\( (0, -6) \)[/tex] and [tex]\( (1, -4) \)[/tex].
- Extend this line in both directions and ensure it covers the entire graph.
7. Verify with More Points (Optional):
- You can verify the accuracy by choosing another [tex]\( x \)[/tex]-value, say [tex]\( x = 2 \)[/tex]:
- Plug [tex]\( x = 2 \)[/tex] into the equation [tex]\( y = 2(2) - 6 \)[/tex], which gives [tex]\( y = 4 - 6 = -2 \)[/tex].
- Plot the point [tex]\( (2, -2) \)[/tex] to ensure it lies on the line.
- Similarly, verify with a negative [tex]\( x \)[/tex]-value, say [tex]\( x = -1 \)[/tex]:
- Plug [tex]\( x = -1 \)[/tex] into the equation [tex]\( y = 2(-1) - 6 \)[/tex], which gives [tex]\( y = -2 - 6 = -8 \)[/tex].
- Plot the point [tex]\( (-1, -8) \)[/tex] to ensure it lies on the line.
Your graph should look like this:
```
y
|
10 | .
9 | .
8 | .
7 | .
6 |
5 | .
4 | .
3 | .
2 | .
1 | .
0 o--------------------------------------| x
-1 | .
-2 | .
-3 | .
-4 o (1, -4)
-5 |
-6 o (0, -6)
-7 |
-8 o (-1, -8)
-9 |
-10 |
```
This shows the line [tex]\( y = 2x - 6 \)[/tex] graphed on the coordinate plane. The line crosses the y-axis at [tex]\( y = -6 \)[/tex] and rises with a slope of [tex]\( 2 \)[/tex].
1. Identify the Equation and Components:
- The given equation is [tex]\( y = 2x - 6 \)[/tex].
- The equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where:
- [tex]\( m \)[/tex] is the slope (rate of change) of the line.
- [tex]\( b \)[/tex] is the y-intercept (the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]).
2. Determine the Slope and Y-Intercept:
- [tex]\( m = 2 \)[/tex] (slope), which means that for every unit increase in [tex]\( x \)[/tex], [tex]\( y \)[/tex] increases by 2 units.
- [tex]\( b = -6 \)[/tex] (y-intercept), which means the line crosses the y-axis at [tex]\( y = -6 \)[/tex].
3. Plot the Y-Intercept:
- Locate the point [tex]\( (0, -6) \)[/tex] on the graph and put a point there. This is the y-intercept.
4. Use the Slope to Find Another Point:
- Starting from the y-intercept [tex]\( (0, -6) \)[/tex], use the slope [tex]\( m = 2 \)[/tex] to find another point.
- Since the slope is [tex]\( 2 \)[/tex], move up 2 units in the y-direction and 1 unit in the x-direction.
- Doing this, from [tex]\( (0, -6) \)[/tex], we move to the point [tex]\( (1, -4) \)[/tex].
5. Plot the Second Point:
- Locate the point [tex]\( (1, -4) \)[/tex] on the graph and put a point there.
6. Draw the Line:
- Draw a straight line passing through the points [tex]\( (0, -6) \)[/tex] and [tex]\( (1, -4) \)[/tex].
- Extend this line in both directions and ensure it covers the entire graph.
7. Verify with More Points (Optional):
- You can verify the accuracy by choosing another [tex]\( x \)[/tex]-value, say [tex]\( x = 2 \)[/tex]:
- Plug [tex]\( x = 2 \)[/tex] into the equation [tex]\( y = 2(2) - 6 \)[/tex], which gives [tex]\( y = 4 - 6 = -2 \)[/tex].
- Plot the point [tex]\( (2, -2) \)[/tex] to ensure it lies on the line.
- Similarly, verify with a negative [tex]\( x \)[/tex]-value, say [tex]\( x = -1 \)[/tex]:
- Plug [tex]\( x = -1 \)[/tex] into the equation [tex]\( y = 2(-1) - 6 \)[/tex], which gives [tex]\( y = -2 - 6 = -8 \)[/tex].
- Plot the point [tex]\( (-1, -8) \)[/tex] to ensure it lies on the line.
Your graph should look like this:
```
y
|
10 | .
9 | .
8 | .
7 | .
6 |
5 | .
4 | .
3 | .
2 | .
1 | .
0 o--------------------------------------| x
-1 | .
-2 | .
-3 | .
-4 o (1, -4)
-5 |
-6 o (0, -6)
-7 |
-8 o (-1, -8)
-9 |
-10 |
```
This shows the line [tex]\( y = 2x - 6 \)[/tex] graphed on the coordinate plane. The line crosses the y-axis at [tex]\( y = -6 \)[/tex] and rises with a slope of [tex]\( 2 \)[/tex].
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
