Equations

Algebraic equations involving two unknowns can readily be shown on a graph. Figure 7 shows a plot of the equation x + y = 5. The equation is solved for corresponding sets of values of x and y that satisfy the equation. Each of these points is plotted and the points connected. The graph of x + y = 5 is a straight line.

Figure ? Plot of x + y = 5

The x-intercept of a line on a graph is defined as the value of the x-coordinate when the y-coordinate is zero. It is the value of x where the graph intercepts the x-axis. The y-intercept of a graph is defined as the value of the y-coordinate when the x-coordinate is zero. It is the value of y where the graph intercepts the y-axis. Thus, the x-intercept of the graph of x + y = 5 is +5. For a linear equation in the general form ax + by = c, the x-intercept and y-intercept can also be given in general form.

Any algebraic equation involving two unknowns of any function relating two physical quantities can be plotted on a Cartesian coordinate graph. Linear equations or linear functions plot as straight lines on Cartesian coordinate graphs. For example, x + y = 5 and f(x) = 3x + 9 plot as straight lines. Higher order equations or functions, such as quadratic equations or functions and exponential equations, can be plotted on Cartesian coordinate graphs. Figure 8 shows the shape of the graph of a typical quadratic equation or function. This shape is called a parabola. Figure 9 shows the shape of the graph of a typical exponential equation or function.

Figure 8 Cartesian Coordinate Graph of Quadratic Equation or Function

Figure 9 Cartesian Coordinate Graph of Exponential Equation or Function