Which ordered pairs are on the line 4x−3y=84x−3y=8 ?
Select each correct answer.
(−1,4)
(1,−4/3)
(3/2,−2/3)
(−4,−8)
I know that one is (1,4/3) but I thought the other was (2,0) and it is not up their. Help please!
well, your equation has a typo (it has two = signs, and that 84x cannot be right!). Aha -- it appears that you have duplicated the equation
4x-3y = 8
Clearly (1,4/3) does not fit, but
(1,-4/3) does work, since
4(1)-3(-4/3) = 4+4 = 8
4(3/2)-3(-2/3) = 6+2 = 8
4(-4)-3(-8) = -16+24 = 8
Now. was that so hard?
Yes yes it was hard :D
To find the ordered pairs on the line 4x - 3y = 8, you can substitute different values for x or y and solve for the corresponding variable.
Let's start by substituting x = -1:
4(-1) - 3y = 8
-4 - 3y = 8
-3y = 12
y = -4
So, (-1, -4) is on the line.
Now, let's substitute x = 1:
4(1) - 3y = 8
4 - 3y = 8
-3y = 4
y = -4/3
So, (1, -4/3) is on the line.
Next, let's substitute x = 3/2:
4(3/2) - 3y = 8
6 - 3y = 8
-3y = 2
y = -2/3
So, (3/2, -2/3) is on the line.
Lastly, let's substitute x = -4:
4(-4) - 3y = 8
-16 - 3y = 8
-3y = 24
y = -8
So, (-4, -8) is on the line.
Therefore, the ordered pairs that are on the line 4x - 3y = 8 are:
(-1, -4), (1, -4/3), (3/2, -2/3), and (-4, -8).
To determine which ordered pairs are on the line defined by the equation 4x - 3y = 8, we can start by rewriting the equation in the form y = mx + b, where m represents the slope and b represents the y-intercept. In this case, we have:
4x - 3y = 8
Rearranging the terms, we get:
-3y = -4x + 8
Dividing through by -3, we obtain:
y = (4/3)x - 8/3
Now that we have the equation in slope-intercept form, we can identify the slope (m = 4/3) and the y-intercept (b = -8/3).
To find additional points on the line, you can substitute different x-values into the equation and solve for the corresponding y-values.
Let's test the given options:
1. (-1, 4):
Plugging x = -1 into the equation, we have:
y = (4/3)(-1) - 8/3
y = -4/3 - 8/3
y = -12/3
y = -4
So, (-1, 4) is not on the line.
2. (1, -4/3):
Plugging x = 1 into the equation, we have:
y = (4/3)(1) - 8/3
y = 4/3 - 8/3
y = -4/3
So, (1, -4/3) is on the line.
3. (3/2, -2/3):
Plugging x = 3/2 into the equation, we have:
y = (4/3)(3/2) - 8/3
y = 6/3 - 8/3
y = -2/3
So, (3/2, -2/3) is on the line.
4. (-4, -8):
Plugging x = -4 into the equation, we have:
y = (4/3)(-4) - 8/3
y = -16/3 - 8/3
y = -24/3
y = -8
So, (-4, -8) is not on the line.
Therefore, the correct options are:
- (1, -4/3)
- (3/2, -2/3)