GRAPHING LINEAR EQUATIONS COMMON MISTAKES
1
10/20/2009
Graphing-Coordinate System and Plotting Points How to Plot Points The grid containing the x and y axes is called the Cartesian Coordinate Plane. Points are plotted by using horizontal and vertical distances from the starting point called the origin (where the x and y axes intersecthas the coordinates (0,0) ). A point’s coordinates are labeled (x, y) where x = distance right or left on the x-axis and y = distance up or down from the x-axis. To graph the point, start at the origin, (0,0), go the x distance on the x-axis and then from that location, go the y distance above or below your mark.
2
Common Mistakes
Confusing the x- and ydistances/directions. Plotting A(3, 2), B(-1, 5), C(-4, 0), D(2, -3) and E(5, -2) would look like…
Complete Manual: ..\Linear Function Review.docx and ..\Graphing Linear Equations Review.docx To view; right click an open the hyperlink
B C E
A D
10/20/2009
Graphing-Understanding Slope How Slope affects the graph’s direction
Recall: Slope, m, relates the ‘slant’ of a line… m > 0 slant: upward m = 0 slant: horizontal m < 0 slant: downward m = undefined : vertical Equations use slope, m, in their formats (i.e. SlopeIntercept, and Point-Slope)
3
Common Mistakes
Incorrectly identifying slope or graphing it. Not realizing slope, m, really is m = vertical change horizontal change
Example 1:
Complete Manual: ..\Linear Function Review.docx and ..\Graphing Linear Equations Review.docx To view; right click an open the hyperlink
y = 3x + 2
The slope is 3 NOT 3x. Example 2:
8x + 3y = 11 Solving for y finds the slope is − 8 . 3 10/20/2009
Graphing-Slope (continued) Identifying Slope to Graph a Linear Function Slope has many definitions. y −y m = x − x for 2 points m = rise = dy where the
2
1
2
1
run
dx
d means ‘change in the x distance or change in the y’ distances.
Common Mistakes
Example 1: Identify the slope in
Incorrect: The slope is 3x. Correct: The slope is 3.
Graphing requires at least one point and the slope or two points.
Incorrectly identifying slope or graphing it. Not realizing slope, m, really is m = vertical change horizontal change
y = 3x − 2
Example 2: Find the slope: 8x + 3y = 11 Incorrect: The slope is 8 Correct: Solving for y gives the slope, m, as −8 m=
3
4
Complete Manual: ..\Linear Function Review.docx and ..\Graphing Linear Equations Review.docx To view; right click an open the hyperlink
10/20/2009
Graphing-Slope (continued) Graphing a Linear Function using it’s Slope
The form y= mx + b, known as the Slope-Intercept Form, is easily graphed. Step 1: Start by solving the equation into y=mx+b form, where m= slope (put into fraction form and b=y-intercept.) Step 2: Plot (0, b) Step 3: Use the slope m to find another point.. m>0, m=0, m
