can anyone please help me with understanding how to graph equations such as 2x-3y=9, 6x-5y+20=0, -2x=2y +5, and y=-2.
Thnx!
assistance needed
Of course! I can help you understand how to graph equations step-by-step. Let's start with the equation 2x - 3y = 9.
Step 1: Convert the equation to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
2x - 3y = 9
-3y = -2x + 9
y = (2/3)x - 3
Step 2: Determine the slope (m) and y-intercept (b).
The slope (m) is the coefficient of x, which is 2/3.
The y-intercept (b) is the constant term, which is -3.
Step 3: Plot the y-intercept.
Start by plotting the point (0, -3) on the graph, which is the y-intercept.
Step 4: Use the slope to find additional points.
To find the next point, move right by 3 units (numerator of slope) and up by 2 units (denominator of slope) from the y-intercept.
This gives you the point (3, -1).
Step 5: Draw a straight line passing through the two points.
Connect the points (0, -3) and (3, -1) with a straight line. Extend the line as needed.
Now let's move on to the equation 6x - 5y + 20 = 0.
Step 1: Convert the equation to slope-intercept form (y = mx + b).
6x - 5y + 20 = 0
-5y = -6x - 20
y = (6/5)x + 4
Step 2: Determine the slope (m) and y-intercept (b).
The slope (m) is the coefficient of x, which is 6/5.
The y-intercept (b) is the constant term, which is 4.
Step 3: Plot the y-intercept.
Start by plotting the point (0, 4) on the graph, which is the y-intercept.
Step 4: Use the slope to find additional points.
To find the next point, move right by 5 units (denominator of slope) and up by 6 units (numerator of slope) from the y-intercept.
This gives you the point (5, 10).
Step 5: Draw a straight line passing through the two points.
Connect the points (0, 4) and (5, 10) with a straight line. Extend the line as needed.
Now let's work on the equation -2x = 2y + 5.
Step 1: Convert the equation to slope-intercept form (y = mx + b).
-2x = 2y + 5
2y = -2x - 5
y = (-2/2)x - (5/2)
y = -x - (5/2)
Step 2: Determine the slope (m) and y-intercept (b).
The slope (m) is the coefficient of x, which is -1.
The y-intercept (b) is the constant term, which is -5/2.
Step 3: Plot the y-intercept.
Start by plotting the point (0, -5/2) on the graph, which is the y-intercept.
Step 4: Use the slope to find additional points.
To find the next point, move right by 1 unit and down by 1 unit from the y-intercept.
This gives you the point (1, -3/2).
Step 5: Draw a straight line passing through the two points.
Connect the points (0, -5/2) and (1, -3/2) with a straight line. Extend the line as needed.
Lastly, let's examine the equation y = -2.
This equation is already in slope-intercept form, where the slope (m) is 0 and the y-intercept (b) is -2.
Step 1: Plot the y-intercept.
Start by plotting the point (0, -2) on the graph, which is the y-intercept.
Step 2: Draw a horizontal line passing through the point (0, -2).
Since the slope is 0, the line is horizontal and all the other points on the line have a y-coordinate of -2.
I hope this step-by-step explanation has helped you understand how to graph these equations. Let me know if you have any further questions!
Of course! I'd be happy to help you understand how to graph these equations. Graphing equations can be a useful way to visualize and analyze mathematical relationships.
To graph an equation, we usually start by rewriting it in the slope-intercept form, which is in the form of y = mx + b. This form helps us determine the slope (m) and y-intercept (b) of the line.
Now, let's go through each equation one by one and graph them.
1. Equation: 2x - 3y = 9
Start by isolating y on one side of the equation:
-3y = -2x + 9
Divide both sides by -3 to solve for y:
y = (2/3)x - 3
Since the slope-intercept form is y = (2/3)x - 3, we can identify:
- Slope (m) = 2/3 (rise of 2 and run of 3)
- Y-intercept (b) = -3
To graph the line:
- Plot the y-intercept at (0, -3) on the y-axis.
- Use the slope to identify the next points. For example, if the slope is 2/3, go up 2 units and move 3 units to the right from the y-intercept to find the next point, and so on.
- Connect the points to create a straight line.
2. Equation: 6x - 5y + 20 = 0
Start by isolating y on one side of the equation:
-5y = -6x - 20
Divide both sides by -5 to solve for y:
y = (6/5)x + 4
The slope-intercept form is y = (6/5)x + 4:
- Slope (m) = 6/5 (rise of 6 and run of 5)
- Y-intercept (b) = 4
To graph the line:
- Plot the y-intercept at (0, 4) on the y-axis.
- Use the slope to identify the next points. For example, if the slope is 6/5, go up 6 units and move 5 units to the right from the y-intercept to find the next point, and so on.
- Connect the points to create a straight line.
3. Equation: -2x = 2y + 5
Start by isolating y on one side of the equation:
2y = -2x - 5
Divide both sides by 2 to solve for y:
y = (-2/2)x - (5/2)
y = -x - (5/2)
The slope-intercept form is y = -x - (5/2):
- Slope (m) = -1 (rise of -1 and run of 1)
- Y-intercept (b) = -5/2
To graph the line:
- Plot the y-intercept at (0, -5/2) on the y-axis.
- Use the slope to identify the next points. For example, if the slope is -1, go down 1 unit and move 1 unit to the right from the y-intercept to find the next point, and so on.
- Connect the points to create a straight line.
4. Equation: y = -2
This equation is already in the slope-intercept form, y = mx + b.
- Slope (m) = 0
- Y-intercept (b) = -2
To graph the line:
- Since the slope is 0, the line is a horizontal line passing through y = -2.
- Draw a straight line parallel to the x-axis at y = -2.
I hope this explanation helps you understand how to graph these equations. If you have any further questions or need additional assistance, feel free to ask!