Determine whether the equation defines y as a linear function of x. If so, write it in the form
y = mx + b.
6x+√y-7=0
a. y=-6x-7
b. y=-6x+7
c. y=6x
d. y is not a linear function of x
if it has the square root of a variable in it (y^.5), it is not a straight line
To determine if the equation defines y as a linear function of x, we need to rearrange the equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Let's start by isolating the term with √y and move all other terms to the other side of the equation:
√y = 7 - 6x
Now, square both sides of the equation to eliminate the square root:
(√y)^2 = (7 - 6x)^2
Simplifying,
y = (7 - 6x)^2
Expanding the right side,
y = 49 - 84x + 36x^2
As we can see, the equation y = 49 - 84x + 36x^2 does not fit the form y = mx + b. Therefore, the equation does not define y as a linear function of x. Therefore, the correct answer is d. y is not a linear function of x.
To determine whether the equation defines y as a linear function of x, we need to check if the equation can be rearranged into the form y = mx + b.
Let's solve the given equation step by step:
6x + √y - 7 = 0
First, let's isolate the square root term (√y) by moving the other terms to the other side:
√y = 7 - 6x
Next, we need to eliminate the square root by squaring both sides of the equation:
(√y)^2 = (7 - 6x)^2
y = (7 - 6x)^2
Now we have y isolated on one side, but the equation is still not in the standard form y = mx + b. Expanding and simplifying the equation further:
y = (7 - 6x)(7 - 6x)
y = 49 - 42x + 36x^2
As we can see, the equation includes a quadratic term (x^2), which means it is not linear. Therefore, the answer is d. y is not a linear function of x.