Point on Graph of Equation....2

In summary, a point on the graph of an equation is a specific location that satisfies the equation and is represented by an ordered pair (x,y) where x is the input value and y is the corresponding output value. To find a point on the graph, you can choose a value for x and plug it into the equation to solve for y. The x-coordinate represents the input or independent variable, while the y-coordinate represents the output or dependent variable. The number of points needed to graph an equation varies, but generally at least two points are needed for a line and three points for a parabola. Having more points can result in a more accurate graph.
  • #1
mathdad
1,283
1
Determine if the given point lies on the graph of the equation.

(a - 1, a + 1); y = x + 2

Let x = a - 1

Let y = a + 1

y = x + 2

a + 1 = a - 1 + 2

a + 1 = a + 1

Yes, the given point lies on the graph of y = x + 2.

Correct?
 
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  • #2
Checking:

y = x + 2

Let x = a - 1

y = a - 1 + 2

y = a + 1

After plugging x = a - 1 into the linear equation y = x + 2, I found the original value of y given in the point. So, I conclude that the point (a - 1, a + 1) lies on the graph of the equation.

Correct?
 

Related to Point on Graph of Equation....2

What is a point on the graph of an equation?

A point on the graph of an equation is a specific location that satisfies the equation. It is represented by an ordered pair (x,y) where x is the input value and y is the corresponding output value.

How do you find a point on the graph of an equation?

To find a point on the graph of an equation, you can choose a value for x and plug it into the equation to solve for y. The resulting ordered pair (x,y) will be a point on the graph.

What does the x-coordinate represent in a point on the graph of an equation?

The x-coordinate in a point on the graph of an equation represents the input or independent variable. It is the value that is plugged into the equation to determine the corresponding output value.

What does the y-coordinate represent in a point on the graph of an equation?

The y-coordinate in a point on the graph of an equation represents the output or dependent variable. It is the value that is the result of plugging in the x-coordinate into the equation.

How many points do you need to graph an equation?

The number of points needed to graph an equation depends on the complexity of the equation. However, at least two points are needed to create a line, and three points are needed to create a parabola. Generally, the more points you have, the more accurate your graph will be.

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