Lesson 13MA 152, Section 2.1

Rectangular Coordinate System:

Every point on a rectangular

coordinate system is represented by

an ordered pair , (x, y). x and y

are called the coordinates of the point.

Ex 1:

a)In which quadrant(s) do the coordinates of a pointhave the same sign?

b)In which quadrant would the point (-2, 3) be found?

c)The point (12, 0) is found on which axis?

d)What point would be 5 right and 6 down from the origin?

Any equation of the form is a linear equation, because the graph of the equation will be a line. The constants A, B, and C represent real numbers (usually integers).

Graphing Linear Equations:

  1. Make a table. Select a value for x or y and solve for the remaining variable. These are the coordinates of a point on the line.
  2. Select another x or y value and solve for the remaining coordinate.
  3. It is a good idea to find a third point.
  4. Plot the points and connect to make a line. This graph represents all solutions of the linear equation.

Intercepts: If the line intersects the x-axis, that point (a, 0) is called the x-intercept. If the line intersects the y-axis, that point (0, b) is called the y-intercept. Intercepts are often used when graphing an equation.

Ex 2:Graph each linear equation.

What are the intercepts?______

Ex 3: Find the intercepts for the following equation.

Ex 4: Graph each line.

If a and b are real numbers, then

  • The graph of the equation x = a is a vertical line with an x-intercept of (a, 0).
  • The graph of the equation y = b is a horizontal line with a y-intercept of (0, b).

Note: If the equation has only an x or only a y, solve for that variable. Then you will know where the intercept is and be able to graph the line.

Ex 5:A computer is purchased for $980 and is expected to depreciate according to the formula .

a)How much is the computer worth two years after purchase?

b)After how long will the computer be worth only $198?

c)After how many years is the computer worthless? Round to the nearest tenth of a year, if necessary.

Notation for points: Points are labeled using capital letter. Sometimes a point may be written as follows: . This is read 'point P with coordinates of x sub 1 and y sub 1.

To find the distance between two points, the Pythagorean theorem could be used.

The second line is known as the distance formula between two points.

Ex 6:Find the distance between each pair of points.

The midpoint of two point P and Q is the point midway between P and Q. Its coordinates are the average of the x coordinates of P and Q and the average of the y coordinates of P and Q.

The midpoint of is .

Ex 7:Find the midpoint of each pair of points.

Ex 8:Determine is a triangle with the following vertices is an equilateral triangle.

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