Find points of C=5x-4y
The equation C = 5x - 4y represents a linear equation in standard form. To find points on this line, you can arbitrarily assign a value to one variable and solve for the other.
For example, let's assign a value of 0 to x:
C = 5(0) - 4y
C = -4y
Here, we can see that C is directly related to y. So, if we assign different values to y, we can find corresponding values for C:
If y = 0:
C = -4(0) = 0
So one point on the line is (0, 0).
If y = 2:
C = -4(2) = -8
So another point on the line is (0, -8).
If y = -2:
C = -4(-2) = 8
So another point on the line is (0, 8).
By assigning different values to x, you can find more points on the line.
To graph the equation C=5x-4y, we need to find several points that satisfy the equation. To do this, we will assign arbitrary values to x or y and solve for the other variable.
Let's start by assigning a value of zero to x and solve for y:
C = 5(0) - 4y
C = -4y
Now, let's assign different values to C and solve for y:
1. If C = 0:
0 = -4y
Divide both sides by -4:
0 = y, so one point is (0, 0).
2. If C = 5:
5 = -4y
Divide both sides by -4:
-5/4 = y, so another point is (-5/4, 5).
Now let's assign a value of zero to y and solve for x:
C = 5x - 4(0)
C = 5x
Similarly, let's assign different values to C and solve for x:
1. If C = 0:
0 = 5x
Divide both sides by 5:
0 = x, so another point is (0, 0).
2. If C = 4:
4 = 5x
Divide both sides by 5:
4/5 = x, so another point is (4/5, 4).
Therefore, some points on the graph of C=5x-4y are:
(0, 0), (-5/4, 5), (0, 0), and (4/5, 4).
To find the points on the graph of the equation C = 5x - 4y, we need to solve for the values of x and y that satisfy this equation.
Here's how you can find the points:
1. Let's assume that C = 0. By setting C to zero, we will find the values of x and y that correspond to the x-intercepts and y-intercepts of the graph.
So, the equation becomes: 0 = 5x - 4y.
2. Solve this equation for y in terms of x.
Subtract 5x from both sides of the equation to isolate -4y: -5x = -4y.
Divide both sides by -4 to solve for y: y = (5/4)x.
Now we have the equation in slope-intercept form (y = mx + b), where m represents the slope (in this case, 5/4) and b represents the y-intercept (which is zero in this case).
3. Start by choosing a value for x. Let's say x = 0.
Substitute this value into the equation y = (5/4)x.
y = (5/4)(0) = 0.
So, when x = 0, y = 0. This gives us one point on the graph: (0,0).
4. Now let's choose another value for x. Let's say x = 4.
Substitute this value into the equation y = (5/4)x.
y = (5/4)(4) = 5.
So, when x = 4, y = 5. This gives us another point on the graph: (4,5).
5. You can continue this process by choosing different values for x and finding the corresponding values for y.
Here are a few more points you can find:
- When x = -4, y = -5. So, one more point is (-4, -5).
- When x = 8, y = 10. So, another point is (8, 10).
By finding more points, you can plot them on a graph and connect them to create the graph of the equation C = 5x - 4y.