Math 22 Graph of Equation

The Graph of an Equation

The graph of an equation is the set of all points that are solutions of the equation.

In this section, we use point-plotting method. With this method, you construct a table of values that consists of several solution points of the equation

For example, sketch the graph of Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle y=2x+1} . We can construct the table below by plugging points for $x$.

x	0	1	2	3
y=2x+1	1	3	5	7

So, we can sketch the graph from those order pairs.

Intercepts of a Graph

Some solution points have zero as either the $x$-coordinate or the $y$-coordinate. These points are called intercepts because they are the points at which the graph intersects the $x$- or $y$-axis.

 To find $x$-intercepts, let $y$ be zero and solve the equation for $x$.
 
 To find $y$-intercepts, let $x$ be zero and solve the equation for $y$.

Example Find the x-intercepts and y-intercepts of the graph $y=x^{2}-2x$

Solution:
x-intercept: Let $y=0$, so $x^{2}-2x=0$, hence $x(x-2)=0$, therefore, $x=0$ or $x=2$
y-intercept: Let $x=0$, so $y=(0)^{2}-2(0)=0$
Answer: $(0,0)$ and $(2,0)$ are x-intercepts
$(0,0)$ is y-intercept

Circles

 The standard form of the equation of a circle is
 

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x-h)^2+(y-k)^2=r^2}

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