Cartesian Grid Plotting Points y Cartesian Grid Plotting Points B points are ordered pairs, x first, then y, in order Point (x, y) A D x A(4, 6) G B(0, 7) C(-4, -9) F D(3, 0) E(7, -10) C E F(1.5, -6.5) G(-3/2, -7/4) plotting points

x y -3 1 -2 4 1 10 7 y graphing using a table of values x -3 1 -2 4 1 10 7 table graph x-3

x y -7 1 -5 5 3 7 7 y graphing using a table of values 2 x -7 2(0) - 7 = -7 1 -5 2(1) - 7 = -5 5 3 2(5) - 7 = 3 7 7 2(7) - 7 = 7 table graph 2x-7

x y -2 10 6 5 -4 6 -6 y graphing using a table of values 3 x -2(-2)+6 = 10 6 -2(0)+6 = 6 5 -4 -2(5)+6 = -4 6 -6 -2(6)+6 = -6 table graph –2x+6

x y -2 5 4 5 1.5 8 y graphing using a table of values 4 x -1/2(-2)+4=5 4 -1/2(0)+4 = 4 5 1.5 -1/2(5)+4=1.5 8 -1/2(8) + 4 = 0 table graph table graph –2x+6

10 6 y x Features of graphed line x-intercept (3, 0) y-intercept 5 SLOPE: the slope of a line is how quickly it rises or falls. The direction! this line rises 5 every time it steps 3 right the slope is 5/3 x-intercept (3, 0) 10 x y-intercept (0, -5) 5 3 6 or you could say it is 10/6 which is really 5/3 x-intercept: the point where the line crosses the x-axis; in this case (3, 0). y-intercept: the point where the line crosses the y-axis; in this case (0,-5). slope

y x Graph equation without a table 8 EXAMPLE: y-intercept A line can be written in the form: y = mx + b; where m and b are given numbers. the b is the ‘y-intercept’ the m is the ‘slope’ it makes it easy to graph without a table x 8 EXAMPLE: graph y = 2x – 8 y-intercept (0, -8) 2 1 4 plot the y-intercept (0, -8) Plot another point or two using the slope, the rise per run right, of 2/1 or 4/2 or 8/4, etc hint: convert the slope into a fraction slope-intercept form

y 8 x Graph equation without a table 4 y-intercept (0, 6) EXAMPLE: A line can be written in the form: y = mx + b; where m and b are given numbers. the b is the ‘y-intercept’ the m is the ‘slope’ it makes it easy to graph without a table 4 1 y-intercept (0, 6) 2 8 x EXAMPLE: graph y = -2x + 6 plot the y-intercept (0, 6) Plot another point or two using the slope, the rise per run right, of -2/1 or -4/2 or -8/4, etc hint: a rise of –2 is a drop of two slope intercept2

y 5 8 x Graph equation without a table y-intercept (0, 2) EXAMPLE: A line can be written in the form: y = mx + b; where m and b are given numbers. the b is the ‘y-intercept’ the m is the ‘slope’ it makes it easy to graph without a table y-intercept (0, 2) 5 8 x EXAMPLE: plot the y-intercept (0, 2) Plot another point using the slope, the rise per run right, of 5/8. slope intercept 3

Graphing equations in the slope and intercept form; y = mx + b is easy But sometimes the x and the y are on the same side of the equals sign; ax + by = c ; where a, b, and c are given numbers. There are two ways to graph these: do a literal conversion to the y = mx + b slope and intercept form; or do the intercept-intercept method general form

Convert 2x + 4y = 12 subtract 2x from both sides divide both sides by 4 We tend to write the terms with variables in them first; so: literal conversion

intercept-intercept method y Plot equation from General form 2x + 4y = 12 x y 3 x 6 Evaluate for x = 0 2(0) + 4y = 12 4y = 12 y = 12/4 = 3 So (0, 3) is one point ; it is on the y-axis Evaluate for y = 0 2x + 4(0) = 12 2x = 12 x = 12/2 = 6 So (6, 0) is one point; it is on the x-axis intercept-intercept method

Plot equation from General form y Plot equation from General form of course, you can evaluate the x or y for any values you want, but zeros are way easier to calculate. And intercepts are easy to plot too x – 3y = 9 x y -3 x 9 Evaluate for x = 0 (0) – 3y = 9 -3y = 9 y = 9/-3 = -3 So (0, -3) is one point ; it is on the y-axis Evaluate for y = 0 x – 3(0) = 9 x = 9 x = 9 So (9, 0) is one point; it is on the x-axis intercept-intercept2