Graphing Linear Equations
Write the following equation into standard form:
x = y - 5
x - y = -5
Solve equation:
0 = 1/3x - 2
x = 6
Find the slope of a line that passes through the following points:
(-2, 0) and (1, 5)
5/3
Define linear equation.
An equation that forms a line when it is graphed.
Define ellipsis.
The three dots used in a sequence indicating there are more terms in the sequence that are not listed.
Example: 3, 5, 7, 9,...
Convert the following equation into slope-intercept form:
y - 4 = 2(x - 3)
y = 2x - 2
Solve equation:
-7 = 4x + 1
x = -2
Draw a graph to represent an undefined slope.
Graph should have a vertical line unable to pass the vertical line test.
What are 2 other mathematical words similar to the root of an equation?
-the value of the x-intercept
-the solution
-the zero of a function
Evaluate the expression if a = 4, b = -2, and c = -4
|2a + c| + 1
5
Find the x- and y-intercept of the following equation:
x = 5y + 5
x-intercept: (5, 0)
y-intercept: (0, -1)
Solve equation:
0 = 3/4 - 2/5x
15/8 or 1 7/8
Provide the rate of change represented in the relationship below:
x 5 10 15 20
y 2 3 4 5
1/5
Define slope.
The steepness of a line. rise/run
Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.
If y = 22 when x = 8, find y when x = -16
y = 11/4x, -44
Find the x- and y-intercept of the following equation:
2x - 3y = 5
x-intercept: (5/2, 0)
y-intercept: (0, -5/3)
Solve equation:
19 + 3x = 13 + x
x = -3
Find the value of r so the line passes through each pair of points has the given slope:
(12, 10), (-2, r), m = -4
r = 66
Define rate of change.
The amount one quantity changes with respect to a change in another quantity.
A map of North Carolina is scaled so that 3 inches represents 93 miles. How far apart are Raleigh and Charlotte if they are 1.8 inches apart on the map?
55.8 mi
Explain how to find the x-intercept and y-intercept of a graph and summarize how to graph a linear equation.
You may convert equation into either Standard Form (Ax + By = C) or Slope-Intercept Form (y = mx + b), and replace the variable you are not trying to find with "0." Then solve. Then label intercepts onto graph and connect with a straight line.
Solve equation:
3x - 11 = 1/3x - 8
x = 9/8 or 1 1/8
Find the value of r so the line passes through each pair of points has the given slope:
(r, -5), (3, 13), m = 8
3/4
Define each term found in standard form.
Standard Form: Ax + By = C
-Ax & By are variable terms
-C is called a constant
Provide an example of the Transitive Property.
Example: 6 + 9 = 3 + 12 and 3 + 12 = 15, then 6 + 9 = 15