Download Algebra SoL Review: Equations

Algebra SOL Review:
Slope and Variation
I. Calculating Slope given two points or given a graph:
 If given two ordered pairs, use the formula m 
y2  y1
.
x2 x1
rise
.
run
Horizontal lines have a slope of ____________________.
Vertical lines have a ______________________ slope.
Parallel lines have the _________________ slope.
Slopes of perpendicular lines have a product of __________.
 If given a graph, count




Determine the slope of the line that
passes through the points (12, 6)
and (12, -5).
Determine the slope of the line
pictured below.
Look at the lines on the graph to the right.
Which has a positive slope?
Which has a negative slope?
Which has a slope of 0?
Which has an undefined slope?
II. Graphing a line given a point and the slope:
 Plot the given point.
 Use the slope to find a second point.
 Connect to graph the line.
Graph the line passing
through (3, 4) with slope
III. Graphing Equations in Slope-Intercept Form
 y = mx + b
 Start by plotting a point on the y-intercept (b ).
 Use your slope (m ) to rise and run to another point on the line.
 Connect the two points you plotted.
Graph:
2
y   x 8
5
Write an equation for the graph.
2
.
3
IV. Graphing Equations in Standard Form:
 Calculate the x - intercept and y - intercept.
 Plot these two points and connect to graph the line.
Graph the equation 3x – 8y = -24.
The graph to the right is best
represented by which equation?
[A] 5x + 4y = 20
[B] 5x – 4y = 20
[C] 4x + 5y = 20
[D] 4x – 5y = 20
VI. Writing an equation given a point and the slope:
 Use ( x1 , y1 ) and m values given to substitute into y  y1  m( x  x1 ) .
 Solve for y.
Write an equation for the line that
goes through the point (-1, 5) and
has a slope of –2.
Check to see if your equation
makes sense by graphing as we
did in II.
Write an equation for the line that
goes through the point (4, 5) and
3
has a slope of .
4
Check to see if your equation
makes sense by graphing as we
did in II.
V.
Writing an equation given 2 points:
 Calculate slope using the formula m 
y2  y1
x2 x1
.
 Use one of your points as ( x1 , y1 ) and m value given to substitute
into y  y1  m( x  x1 ) .
 Solve for y.
Write an equation for the line that
passes through the points (-3, 6)
and (5, 6).
VI.
Check to see if your equation
makes sense by plotting the two
ordered pairs.
Variation:
Direct Variation:
 y = kx or k 
y
x
 The graph would be a straight line passing through the origin.
 “y” varies directly as “x ”
From the table, determine if y
varies directly as x. If so, write the
equation describing the variation.
x -2 -1 3
5
y 6
3 -9 -15
At a given time and place, the
height of an object varies directly
as the length of its shadow. If a
flagpole 6 meters high casts a
shadow 10 meters long, find the
height of a building that casts a
shadow 45 meters long.
Inverse Variation:
 x  y  k is the form of an inverse variation equation, where k is the
constant
 As input values increase, output values decrease and vice versa
 Graphs of Inverse Variations are not linear
In the table below, determine the
equation of variation and identify if
it is a direct or inverse variation.
X
5
Y
8
A.
B.
C.
D.
40
2
10
1
20 -4
y = 1.6x, Direct
y=1.6x, Inverse
xy  40 , Direct
xy  40 , Inverse
VII. Solving Systems of Linear Inequalities:
 Graph both linear inequalities on the same coordinate grid
a. Easier if put in y = mx + b
b. Shade the “true side” of both lines
c. Line is solid if  or 
d. Line is dotted if  or 
 The solution includes the entire region that is shared by both
inequalities.
Solve the
system by
graphing.
 y  x  3

y  x  6