Graphs

Front 1

Slope-intercept equation

Back 1

y = mx + b

Front 2

Slope

Back 2

Rise/run or (change in x)/(change in y)

Front 3

Graphing a line

Back 3

1. Draw the first point at (0, b) where b is the y-intercept

2. Draw the second point so that the y-coordinate equals the absolute value of the slope, moving up the y-axis if the slope is positive and down the y-axis if the slope is negative

3. Connect the points and extend the line upward if the slope is positive and downward if the slope is negative

Front 4

Deriving a line equation from the coordinates of 2 points

Back 4

1. Find the slope using ((change in y-coordinates)/(change in x-coordinates))

2. Plug the coordinates of one of the points into the equation y = mx + b and solve for b

3. Organize the information into the format y = mx + b

Front 5

Parallel lines

Back 5

Lines with the same slope, e.g. y = 4x + 5, y = 4x -7, and anything in the format y = 4x + b

Front 6

Perpendicular lines

Back 6

Lines whose slopes are negative reciprocals of one another, e.g. y = 4x + 5 and y = -1/4x + 5

Front 7

Graphing an absolute value

Back 7

Reflect any negative y-coordinates over the x-axis so that they are the same numbers but positive

Front 8

Graph of y=x

Back 8

Slope is 1 and line passes through the origin

Front 9

Graphing inequalities

Back 9

Convert the inequality into y = mx + b format like when graphing a line, but:

1. If y is greater than the line equation, everything above the line is allowed

2. If y is less than the line equation, everything below the line is allowed

Front 10

Finding the distance between 2 points on a 2D graph

Back 10

1. Plot the points

2. Draw a right triangle connecting the points

3. Use the Pythagorean Theorem

Front 11

Finding the distance between 2 points on a 3D graph

Back 11

Take the square root of ((x2 - x1)^2) + ((y2-y1)^2) + ((z2-z1)^2)