Math 374 Graphs

Topics Cartesian Plane Methods of Graphing Intercept Slope Scale First Quadrant Inequality Graphs Region

Cartesian Plane Named after Rene Deo Cartes a french mathematician Also a philosopher “I think therefore I am” His goal was to create a “picture” that could show a relationship between two variables. We have one for one variable – the number line.

Notes We recall

Some Facts We only need two points to draw a straight line The point where a graph crosses or touches the x axis is called the x intercept It is found by substituting y = 0 The point where a graph crosses or touches the y axis is called the y intercept It is found by substituting x = 0

Intercept Method Calculate both intercepts. Place on graph and join Example #1: y = 2x – 6 X intercept (y = 0) 0 = 2x – 6 -2x = - 6 x = 3

Intercept Method Now find Y intercept Example #1: y = 2x – 6 Y intercept (x = 0) y = 2 (0) – 6 y = -6

Finding X and Y Intercept Example #2: 5x – 3y = 15 x int (y = 0)  5x – 3(0) = 15 5x = 15 x = 3 y Int (x = 0)  5(0) – 3y = 15 -3y = 15 y = -5

Drawing on Graph Now that you know the x & y intercept, you have two points and now can draw the straight line… do it! Practice plotting with other points…

Plotting. C (-4, -4).... B (-4, 2) D (2, -2) (A 3, 1) Q1 (+,+) Q4 (+,-) Q3 (-,-) Q2 (-,+) A (3,1) B (-4,2) C (-4, -4) D (2, -2)

Standard Form Method All straight lines have a y intercept and a slant called a slope. If the relationship is in standard form we can write it… y = m x + b Slope Y intercept

Y Int Slant Y Int Identifying Slant and Slope

Relationship of y and b It is easy to see how b is the Y intercept; we substitute x = 0 Recall y = mx + b x = 0  y = m(0) + b y = b

Rise, Run & Slope Slope Rise Run Rise Run Slope

Understanding the Slope If m or the slope is 2 this means a rise of 2 and a run of 1 (2 can be written as 2 ) 1 If m = - 5, this means a rise of -5 and right 1 If m= -2 this means rise of -2 right 3 3

Consider y = 2x + 3 We can write the slope 2 as a fraction 2 1 We have a y intercept of 3 This means we have a rise of 2 (up) Run of 1 (right)