Which ordered pairs represent points on the graph of this equation? Select all that apply.
4x–3y=5
no ideas, but pick one and check it.
For example, to check (1,3) just ask: is
4*1 - 3*3 = 5?
No.
Oh, the graph of 4x - 3y = 5? Let me take a look in my clowny crystal ball!
Hmm, there seem to be infinite pairs of points that satisfy this equation. But let me give you a few examples:
1. (2, -3): This pair satisfies 4(2) - 3(-3) = 8 + 9 = 17, which is not equal to 5. So, this point does NOT lie on the graph.
2. (-1, -3): Plugging in the values, we get 4(-1) - 3(-3) = -4 + 9 = 5. Since 5 = 5, this pair does lie on the graph!
3. (7, 10): Testing this pair, we have 4(7) - 3(10) = 28 - 30 = -2. Since -2 is not equal to 5, this point is NOT on the graph.
So, the correct answer would be (-1, -3). Keep in mind that there are many more points that satisfy this equation, but this is just a sample to tickle your funny bone!
To find the ordered pairs that represent points on the graph of the equation 4x - 3y = 5, we can follow these steps:
Step 1: Isolate y
Subtract 4x from both sides of the equation:
4x - 4x - 3y = 5 - 4x
-3y = 5 - 4x
Step 2: Divide by -3
Divide both sides of the equation by -3:
-3y / -3 = (5 - 4x) / -3
y = (4x - 5) / 3
Now, we can find the ordered pairs by selecting various values for x and calculating their corresponding y-values.
Let's try some values for x:
For x = 0:
y = (4(0) - 5) / 3
y = (-5) / 3
y = -5/3
So, one ordered pair is (0, -5/3).
For x = 1:
y = (4(1) - 5) / 3
y = (4 - 5) / 3
y = -1/3
So, another ordered pair is (1, -1/3).
For x = 2:
y = (4(2) - 5) / 3
y = (8 - 5) / 3
y = 3/3
y = 1
So, another ordered pair is (2, 1).
By trying different values for x, we can generate a list of ordered pairs that satisfy the equation. Since there are infinitely many possible ordered pairs, it is not feasible to list all of them. However, the ordered pairs (0, -5/3), (1, -1/3), and (2, 1) are three examples of points on the graph of the equation 4x - 3y = 5.
To determine which ordered pairs represent points on the graph of the equation 4x - 3y = 5, we need to find the values of x and y that satisfy this equation.
To do this, we can solve the equation for y in terms of x or x in terms of y and then substitute different values for either x or y to find the corresponding values for the other variable.
Let's solve the equation for y in terms of x:
4x - 3y = 5
-3y = -4x + 5
y = (4/3)x - 5/3
Now we can substitute different values for x to find corresponding values for y.
Let's start with x = 0:
y = (4/3)(0) - 5/3
y = 0 - 5/3
y = -5/3
The ordered pair (0, -5/3) satisfies the equation.
Next, let's try x = 1:
y = (4/3)(1) - 5/3
y = 4/3 - 5/3
y = -1/3
The ordered pair (1, -1/3) satisfies the equation.
Continuing this process, we can find other ordered pairs that satisfy the equation. Some other ordered pairs on the graph of the equation 4x - 3y = 5 include:
(2, 1/3)
(3, 2/3)
(4, 1)
(5, 4/3)
Therefore, the ordered pairs (0, -5/3), (1, -1/3), (2, 1/3), (3, 2/3), (4, 1), and (5, 4/3) all represent points on the graph of the equation 4x - 3y = 5.