Is the function y=x+5 linear or nonlinear?
linear
All linear functions can be written in the form y = mx + b, where m is the slope and b is the y-intercept (slope-intercept form). Alternatively, a linear function can be expressed in the form y – y0 = m(x – x0), where m is the slope and (x0, y0) is a point on the line (point-slope form).
This function, y = 5/x, is a hyperbola, with a vertical asymptote at x = 0 and horizontal asymptote at y = 0.
To determine whether the function y = x + 5 is linear or nonlinear, we can examine its equation. In a linear function, the variable x appears only with a power of 1 and there are no other terms involving x.
In this case, the equation y = x + 5 indeed satisfies these criteria. The variable x has a power of 1 (since it is not raised to any other power) and there are no additional terms involving x. Therefore, the function y = x + 5 is linear.
To verify this, you can also graph the function. When graphed, a linear function will always be a straight line. Plotting the equation y = x + 5 will result in a straight line with a slope of 1 and y-intercept of 5.
In summary, the function y = x + 5 is linear.