Question

Solve the equation graphically. Check your answer algebraically. $$2-x=-5$$

Short answer

The solution to the equation \(2-x=-5\) by graphical method is \(x=7\). This has been confirmed by substituting \(x=7\) algebraically into the original equation.

Step-by-step solution

Setting up the Graph

First, graph the equation \(y=2-x\). This is a straight line with a slope of -1 and y-intercept of 2. Also, graph the line \(y=-5\). This is a horizontal line that intersects the y-axis at -5. The point where these lines intersect will be the solution.

Finding the Intersection Point

Where the two graphs meet is the solution to the equation. In this case, they intersected when \(x=7\). This means that the graphical solution to the equation \(2-x=-5\) is \(x=7\). This is because when \(x=7\), both \(y=2-x\) and \(y=-5\) meet at one point on the graph.

Verifying Algebraically

To verify the solution, substitute \(x=7\) into the original equation \(2-x=-5\). The expression becomes \(2-7\), which equals -5. Therefore, the solution has been verified algebraically because substituting \(x=7\) into the equation results in a true statement.