We want to find the equation of a line that has a coefficient of x equal to 2/3 and passes through the point (4,-1).
Let the equation of the line be y = (2/3)x + b, where b is the y-intercept.
To find the value of b, we substitute the coordinates of the given point (4,-1) into the equation and solve for b:
-1 = (2/3)(4) + b
-1 = 8/3 + b
b = -1 - 8/3
b = -11/3
Thus, the equation of the line with a coefficient of x equal to 2/3 and passing through the point (4,-1) is y = (2/3)x - 11/3, which can be written as y = (2x - 11)/3 in standard form.
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Verified answer
Answer:
Step-by-step explanation:
We want to find the equation of a line that has a coefficient of x equal to 2/3 and passes through the point (4,-1).
Let the equation of the line be y = (2/3)x + b, where b is the y-intercept.
To find the value of b, we substitute the coordinates of the given point (4,-1) into the equation and solve for b:
-1 = (2/3)(4) + b
-1 = 8/3 + b
b = -1 - 8/3
b = -11/3
Thus, the equation of the line with a coefficient of x equal to 2/3 and passing through the point (4,-1) is y = (2/3)x - 11/3, which can be written as y = (2x - 11)/3 in standard form.
Answer:
Neither of the given equations passes through the point (4, -1) when the coefficient of x is 2/3
Step-by-step explanation:
To determine the correct equation, let's substitute the given point (4, -1) into each of the options and see which one satisfies it.
For the equation y = (2/3)x^(5/3):
Substituting x = 4 into the equation, we get:
y = (2/3)(4)^(5/3)
y = (2/3)(8)
y = 16/3
The point (4, -1) does not satisfy this equation.
For the equation y = (2/3)x^(-11/3):
Substituting x = 4 into the equation, we get:
y = (2/3)(4)^(-11/3)
y = (2/3)(1/2)
y = 1/3
The point (4, -1) also does not satisfy this equation.
Therefore, neither of the given equations passes through the point (4, -1) when the coefficient of x is 2/3