CHAPTER 5:COORDINATES GEOMETRY AND GRAPH

GRAPH LINIER Basically, graph LINEAR equation can be represented by

y = mx + c Where:-

y and x are 2 anus, c is coordinate of interception at y-axis,

m is the gradient of a straight line.

EXAMPLE 1 Get the gradient of the straight line below:

a. Straight line which passing points are A (-2, 0) dan B (0, 4) b. Straight line which passing points are P (-4, 3) dan Q (5, 3) c. Straight line which passing points are L (4, 5) dan M (4, -6)

Then, create the straight line equation.

SOLUTION

SOLUTION

SOLUTION

DISTANCE, MIDPOINT AND GRADIENT OF GRAPH

Example 2

SIMULTANEOUS EQUATION OF 2 GRAPHS OF LINEAR FUNCTION

Solving two simultaneous equation can be done by using graph drawing where the intersection point of a graph will the value for x and y.

Example 3 Given one straight line with the equation y = - x + 3 intersect with another one straight line with the equation y = 2x – 4. By using graph drawing, find the intersection point.

solution Given the first linear equation, y = - x + 3. At x-axis, y = 0. Therefore 0 = - x + 3 or x = 3. Coordinate is (3, 0). At y-axis, x = 0. Therefore y = 0 + 3 or y = 3. Coordinate is (0, 3). Given the second linear equation, y = 2x – 4. At x-axis, y = 0. Therefore 0 = 2x – 4 or x = 2. Coordinate is (2, 0). At y-axis, x = 0. Therefore y = 2(0) – 4 or y = -4. Coordinate is (0, -4).

The graph drawn is as below.

Quadratic graph The general technique for graphing quadratics is the same as for graphing linear equations. However, since quadratics graph as curvy lines (called "parabolas"), rather than the straight lines generated by linear equations, there are some additional considerations. The most basic quadratic is y = x2. When you graphed straight lines, you only needed two points to graph your line, though you generally plotted three or more points just to be on the safe side. However, three points will almost certainly not be enough points for graphing a quadratic, at least not until you are very experienced. For example, suppose a student computes these three points:

Example 4

x -4 -3 -2 -1 0 1 2 3 4

y 16 9 4 1 0 1 4 9 16

Given y = x2. Build a table from x = -4 until x = 4. From the table,

draw a quadratic graph.

Solution

x = -4, y = (-4)2 = 16 x = 1, y = (1)2 = 1

x = -3, y = (-3)2 = 9 x = 2, y = (2)2 = 4

x = -2, y = (-2)2 = 4 x = 3, y = (3)2 = 9

x = -1, y = (-1)2 = 1 x = 4, y = (4)2 = 16

x = 0, y = (0)2 = 0

Table:

The graph drawn is as below.

THE INTERSECTION POINT OF QUADRATIC GRAPH AND LINEAR GRAPH

Example 5 Draw the graph from equation y = 4x2 + 7x – 5 and y = -5x + 20, by using the value of x = -6 until x = 4. From the graph, determine the intersection points.

SOLUTION

The graph drawn is as below

THE INTERSECTION POINT OF 2 CURVES

Example 6 Determine the intersection points from two curves with the equation y = x2 + x –6 and y = –x2 + x +2.

Solution

The graph drawn is as below