Question

Is it linear non linear a function or not a function:


(y + 7) = 3(x - 2)

Answer 1

To determine whether the equation \((y + 7) = 3(x - 2)\) represents a linear function, we can first rearrange it into the standard linear form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the given equation:

\[
y + 7 = 3(x - 2)
\]

First, distribute the 3 on the right side:

\[
y + 7 = 3x - 6
\]

Next, isolate \(y\) by subtracting 7 from both sides:

\[
y = 3x - 6 - 7
\]

Simplifying gives:

\[
y = 3x - 13
\]

Since this is in the form \(y = mx + b\) where \(m = 3\) and \(b = -13\), we can conclude that the equation represents a linear function.

In summary, the equation \((y + 7) = 3(x - 2)\) is a linear function.