Question

functions and lines
solving a linear equation by graphing
here is an equation.
\\(-2x + 2 = -6\\)
draw a graph to help solve the equation. then find the solution to the equation.
solution: \\(x = \square\\)

Explanation:

Step1: Rearrange the equation to slope - intercept form

We start with the equation \(-2x + 2=-6\). We can think of this as finding the \(x\) - value where the function \(y=-2x + 2\) intersects \(y = - 6\). First, let's solve the equation algebraically (we can also use the graphing method, but algebra is straightforward here).
Subtract 2 from both sides of the equation:
\(-2x+2 - 2=-6 - 2\)
\(-2x=-8\)

Step2: Solve for \(x\)

Divide both sides of the equation \(-2x=-8\) by \(-2\):
\(x=\frac{-8}{-2}\)
\(x = 4\)

If we were to graph \(y=-2x + 2\) (a linear function with slope \(-2\) and \(y\) - intercept \(2\)) and \(y=-6\) (a horizontal line), the \(x\) - coordinate of their intersection point would be \(x = 4\).

Answer:

\(x = 4\)