Question

Use the graph of \(y=-2 x+4\) to solve the inequality \(-2 x+4>0 .\) Explain your reasoning.

Short answer

The solution to the inequality \(-2x + 4 > 0\) is \(x < 2\).

Step-by-step solution

Formulate Linear Equation

Transform the inequality into a linear equation. This gives us the equation \(y = -2x + 4\).

Graphical Representation

When graphing this equation, it becomes clear that it is a straight line with a y-intercept at 4 and a slope of -2. This means, for every increase of 1 in x, y decreases by 2.

Solve Inequality

To solve the inequality \(-2x+4 > 0\), we should look to the graphical representation. The inequality represents all the y-values which are greater than the y-values of the line. Since the slope of the line is negative, the line is going down as x increases. This means that the inequality is true for all x-values where the line is above the x-axis. Looking at the graph, this is where \(x < 2\).