Question

For a given input value \[x\], the function \[g\] outputs a value \[y\] to satisfy the following equation. \[-4x-6=-5y 2\] write a formula for \[g(x)\] in terms of \[x\].

Answer 1

To find the function g(x) in terms of x, given -4x - 6 = -5y, solve the equation for y to obtain g(x) = (4x + 6)/5. A graph can then illustrate the function by plotting (x,y) data pairs.

Step-by-step explanation:

To write a formula for g(x) in terms of x, given -4x - 6 = -5y, we start by isolating y on one side of the equation. This involves adding 6 to both sides of the equation to get -4x = -5y + 6, and then dividing through by -5 to solve for y:

y = ​(​4x + 6)​/​5

Now, we have expressed the function g as dependent on the input value x: g(x) = ​(​4x + 6)​/​5. To understand this function better, we can plot a graph of the relationship between x and y by calculating specific (x,y) data pairs and drawing the resulting line or curve.