Question

Decide whether 2 is the \(x\) -intercept or the \(y\) -intercept of the line \(y=2 x+2\) Explain your choice.

Short answer

2 is the y-intercept of the line \(y=2x+2\), not the x-intercept.

Step-by-step solution

Identify the y-intercept

The y-intercept is the constant term in the equation, which is the value of the line crosses the y-axis. In the equation \(y = 2x + 2\), '2' is the y-intercept as it is the point where the line crosses the y-axis when x = 0.

Check if 2 is the x-intercept

The x-intercept is the value of x when y = 0. Substitute y = 0 in the given equation which yields \(0 = 2x + 2\). Solving this equation gives \(x = -1\). So, '2' is not the x-intercept.

Conclusion

From the above steps, it's clear that '2' is the y-intercept and not the x-intercept of the line. Because when x=0, y=2.