Question

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. (If an answer does not exist, enter DNE.) 4x + 2y = 7

Answer 1

Answer:

Yes, the equation defines y as a linear function of x. The slope intercept form of the provided function is $y=-2x+\frac{7}{2}$.

Step-by-step explanation:

Consider the provided equation.

$4x+2y=7$

Linear equation or function is the function having two variables and the maximum value of the exponent is 1. In the provided equation we have two variables, where the maximum value of the exponent is 1.

Thus, the provided function is a linear function.

Now write it in the form of $y = mx+b$.

Consider the provided equation.

$4x+2y=7$

Subtract 4x from both the sides.

$4x+2y-4x=7-4x$

$2y=-4x+7$

Now divided both the sides by 2.

$\frac{2y}{2}=\frac{-4x}{2}+\frac{7}{2}$

$y=-2x+\frac{7}{2}$

Hence, the slope intercept form of the provided function is $y=-2x+\frac{7}{2}$.