Question

here is an equation.
\\(-2x + 2 = -6\\)
draw a graph to help solve the equation. then find the solution to the equation.

Explanation:

Step1: Rewrite the equation as a function

We can rewrite the equation \(-2x + 2=-6\) as a linear function \(y=-2x + 2\) and we want to find where \(y=-6\) (since we are solving \(-2x + 2=-6\), which is equivalent to finding the \(x\)-value when \(y = - 6\) for the function \(y=-2x+2\)).

Step2: Find two points on the line \(y=-2x + 2\)

• When \(x = 0\), \(y=-2(0)+2=2\). So one point is \((0,2)\).
• When \(x = 1\), \(y=-2(1)+2=0\). So another point is \((1,0)\).

We can plot these two points \((0,2)\) and \((1,0)\) on the coordinate plane and draw the line.

Step3: Find the \(x\)-value when \(y=-6\)

We can also solve the equation algebraically to find the solution.
Start with the equation \(-2x+2=-6\).
Subtract 2 from both sides: \(-2x+2 - 2=-6 - 2\), which simplifies to \(-2x=-8\).
Divide both sides by \(-2\): \(\frac{-2x}{-2}=\frac{-8}{-2}\), so \(x = 4\).
(To use the graph, we would look for the point on the line \(y =-2x + 2\) where \(y=-6\). Substituting \(y=-6\) into \(y=-2x + 2\) and solving gives the same result as the algebraic method.)

Answer:

The solution to the equation \(-2x + 2=-6\) is \(x = 4\).