Coordinate Geometry

Definition  Coordinate grid – a used to locate a point by its distances from 2 intersecting straight lines

Definition  x axis – a horizontal number line on a coordinate grid x

Definition  y axis – a vertical number line on a coordinate grid y

Definition  Coordinates – an ordered pair of numbers that give the location of a point on a grid. (3, 4)

Hint  The first number is always the x or first letter in the alphabet. The second number is always the y the second letter in the alphabet (3,4)

How to Plot Ordered Pairs  Step 1 – Always find the x value first, moving horizontally either right (positive) or left (negative) (2, 3) y x

How to Plot Ordered Pairs  Step 2 – Starting from your new position find the y value by moving vertically either up (positive) or down (negative) (2, 3) y x

How to Find Ordered Pairs  Step 1 – Find how far over horizontally the point is by counting to the right (positive) or the left (negative) (5, 4) y x

How to Find Ordered Pairs  Step 2 – Now count how far vertically the point is by counting up (positive) or down (negative) (5,4) y x

What is the ordered pair? (3,5) y x

What is the ordered pair? (2,6) y x

What is the ordered pair? (4,0) y x

Quadrants There are 4 quadrants.

Four Quadrants Grid  If the x is negative you move to the left of the x = -2 y x

Four Quadrants Grid  If the y is negative you move down below the zero y = -3 y x

How to Plot in 4 Quadrants  Step 1 - Plot the x number first moving to the left when the number is negative (-3, -2) y x

How to Plot in 4 Quadrants  Step 2 - Plot the y number moving from your new position down 2 when the number is negative (-3, -2) y x

How to Plot in 4 Quadrants  When x is positive and y is negative, plot the ordered pair in this manner (2, -2) y x

How to Plot in 4 Quadrants  When x is negative and y is positive, plot the ordered pair in this manner (-2, 2) y x

Plot This Ordered Pair (-3, -3) y x

Plot This Ordered Pair (-1, 2) y x

Plot This Ordered Pair (1, -1) y x

Linear Graphs by Mausmi Jadhav

SLOPE  Mausmi Jadhav Khan

Slope Slope is the steepness of a line. It is represented by rise over run. Formula:  Mausmi Jadhav Khan

Slope Slope describes the direction of a line.  Mausmi Jadhav Khan

Special Slopes Horizontal lines –Slope = zero Vertical lines –Slope = undefined Parallel lines –Slopes are the same. Intersecting lines –Slopes are different and not perpendicular. Perpendicular lines –Slopes are the negative reciprocal of each other.

Slope (m) NEGATIVE SLOPE (-) POSITIVE SLOPE (+)  Mausmi Jadhav Khan

Sign of the Slope Which have a positive slope? Green Blue Which have a negative slope? Red Pink Orange Undefined Zero Slope  Mausmi Jadhav Khan

Slope of a Line x y This line has a slope. Take two points on this line. x 2, y 2 x 1, y 1 Rise = vertical distance Run = horizontal distance Slope (m) = rise = y 2 – y 1 run x 2 – x 1 Name the points.  Mausmi Jadhav Khan

Step – by – Step Guide Visual Instruction  Mausmi Jadhav Khan

Find the slope of the given line: (3, -8) (-5, 0) x 1, y 1 x 2, y 2 To find slope: m = y 2 – y 1 x 2 – x 1 = – 3 = 8 -8 Use abc on the calculator 8 _| -8 m = -1 1 mark to write the formula 1 mark to substitute values 1 mark to evaluate values 1 mark for answer

x-axis y-axis Find the slope between (-3, 6) and (5, 2) Rise Run == (-3, 6) (5, 2)

Calculate the slope between (-3, 6) and (5, 2) x 1 y 1 x 2 y 2 We use the letter m to represent slope m  Mausmi Jadhav Khan

Find the Slopes (5, -2) (11, 2) (3, 9) Brown Orange Green  Mausmi Jadhav Khan

Find the slope between (5, 4) and (5, 2). STOP This slope is undefined. x 1 y 1 x 2 y 2  Mausmi Jadhav Khan

x y Find the slope between (5, 4) and (5, 2). Rise Run -2 0 Undefined ==

Find the slope between (5, 4) and (-3, 4). This slope is zero. x 1 y 1 x 2 y 2  Mausmi Jadhav Khan

x y Rise Run 0 -8 Zero == Find the slope between (5, 4) and (-3, 4).

From these results we can see...  The slope of a vertical line is undefined.  The slope of a horizontal line is 0.  Mausmi Jadhav Khan

POINT-SLOPE FORM  Mausmi Jadhav Khan

Point – Slope Form y – y 1 = m (x – x 1 ) y 2 – y 1 = m (x 2 – x 1 ) REPLACE “2”  Mausmi Jadhav Khan

Point – Slope Form y – y 1 = m (x – x 1 ) slope y - coordinate x - coordinate  Mausmi Jadhav Khan

Step – by – Step Guide Visual Instruction  Mausmi Jadhav Khan

Write the point – slope form of the equation y – 6 = 2(x – 1) slope y - coordinatex - coordinate Answer: m = 2 and (1, 6) y + 4 = 2(x – 8) 5 Answer: m = 2 and (8, -4) 5  Mausmi Jadhav Khan