Question

Is the graph of y = x² + 2 a straight line? Explain.

O No. The graph does not pass through (0, 0), so it is not a straight line.
O No. The graph passes through the points (0, 2), (1, 3), and (2, 6), which do not all lie on a straight line.
O Yes. The graph passes through (0, 0), so it is a straight line.
O Yes. The graph passes through the points (0, 2), (1, 3), and (2, 6), which all lie on a straight line.

Answer 1

Answer: No, the graph of y = x² + 2 is not a straight line. The graph is a parabola that opens upwards and has its vertex at (0, 2).

A straight line is defined by a linear equation, which is an equation that can be written in the form y = mx + b, where m and b are constants. In this equation, the coefficient of x (m) represents the slope of the line, and the constant term (b) represents the y-intercept. A straight line has a constant slope, which means that the rate of change of y with respect to x is constant.

In the case of y = x² + 2, the coefficient of x (x) is not a constant, but rather a variable, which means that the slope of the line changes as x changes. The graph of y = x² + 2 is a parabolic shape that opens upwards and has its vertex at (0, 2). The slope of the graph is not constant, but rather increases as x increases. This means that the graph does not represent a straight line, but rather a parabolic curve.

Explanation: