XY plane

The XY plane enables algebraic functions to be plotted geometrically. We can plot lines on an xy plane by inputting an x value and determining its corresponding y value. X indicates a position on the horizontal axis and y indicates a position on the vertical axis. With these two coordinates, a point may be located anywhere in two dimensional space.

Equations plotted on x y planes are called functions. Let’s look at the shape of each algebraic equation. To do this, we can set each relationship equal to y and plot their corresponding values on an x y plane:

y=c would resemble a horizontal line. Every x equals c, there’s no x so it’s a straight line.

Y=x, makes a diagonal line. Every x equals y.

Y=BX creates a sloped line, at a slope of b.

Y=Ax^2, produces a parabola and where a determines the width of the parabola.

CURVES

Here are equations of other common curves:

Inverse 1/x

Square root 2√x

Square x^2

Cube root 3√x

Cube x^3

Exponential b^x

Logarithmic logb x

As we add constants to these terms, the equations become more complex.

Common equations are linear quadratic and cubic. These are Equations with one two and three as the highest exponents. Each increase in the highest exponent value minus one indicates the number of curves of a line. Quadratic is two it has one curve. Cubic is three it has two curves.

Functions enable us to determine the shape of a line or a curve with only a few pieces of information. For example, with only two points, we can determine the slope of a line between the points and any other value in either direction. B is the slope of the line. Y=BX+c, is a general equation of a line. the c value is where the line crosses the y axis.

For squared functions, the standard form: y=ax^2+bx+c

Any arrangement of constants where the highest exponent of x is two.

For cubic functions the form is x cubed minus ax plus b. Mathematicians figured out all cubic functions may be reduced to this form from the longer form of a x cubed plus b x squared plus Cx plus d.

Okay that’s the general idea of how to plot points on the xy plane.