Which of the following has a graph that is a straight line?

equation 1: y = 4x3 + 6
equation 2: y = 5x − 4.5
equation 3: y2 = x − 1
equation 4: y = 2x2 + 6

The function of a straight line is called Affine function. The general form of its equation is y = mx + b, in which m represents the slope, b the y-intercept, and y and x coordinates of a point.

The equation 1: y=4x^3 + 6 is from the form y=mx^3 + b, which represents a cubic parabola, not a straight line. So Equation 1 is rejected.

Equation 2: y = 5x - 4.5 is from the form y = mx + b. This form of equation, as we said before, is the equation which represents a straight Line. So equation 2 is approved.

Equation 3: y^2 = x - 1 is from the form y^2 = x. This form of equation represents a parabola (Not a normal one. The peak of this parabola is on Y'Y, not on X'X as y=x^2). So equation 3 is rejected.

Equation 4: y = 2x^2 + 6 is from the form y = x^2. This form of equation represents a parabola. So equation 4 is rejected.

We can conclude that equation 2 has a graph that is a straight line.

I've added a picture under the answer representing the 4 equations.

Hope this Helps! :)