GRAPHING EQUATIONS
GOALS
1.
describe
and graph directions using wind directions and angles
2.
understand
and graph horizontal and vertical lines and their equations
3.
use
inequalities to describe regions restricted by horizontal and vertical lines
4.
find
and use equations of the form y = i + sx using the slope and y-intercept
5.
graph
equations of the form y = i + sx
6.
solve
equations of the form a + bx = c + dx
7.
understand
the meaning of slope in different contexts
8.
understand
how to find the intersection point of two lines, algebraically and graphically
9.
understand
the graph of a line in the coordinate plane
10.
model
a problem situation and translate it to a graph or an equation
11.
choose
an appropriate way to solve equations
12.
understand
the similarities between graphic and algebraic strategies
1.
One way to indicate a direction from a point
on a map is to indicate one of the eight
directions found on a
compass rose: N, NE, E, SE, S, SW, W,
and NW.
2.
Another
way is to use degree measurements; beginning with 0° for north, and measuring clockwise up to 360°.
1.
In a coordinate system, the horizontal axis is the x-axis, the vertical
axis is the y-axis,
and these two axes intersect
at the point (0,0), called the origin.
2.
The
location of a point is given by the x- and y- coordinates in an ordered pair
(x,y).
3.
When
points are on a vertical line, the x-coordinate does not change and can be
described by equations such as x = 1, x = 8, and x = -3 .
4.
When
points are on a horizontal line, the y-coordinate does not change and can be
described by equations such as y = -5, y = 0, and y = 3.
5.
Inequalities
can be used to describe a region. For
example, 1 < x < 3 and –2 < y
< 3 describes a 2 by 5 rectangular
region.
SECTION C: DIRECTIONS AS PAIRS
OF NUMBERS
1.
A
directional pair such as [+3,+2] or [+1,-1] can indicate a direction from a
point.
The first number is the
horizontal component, and the second is the vertical component.
2.
All
direction pairs in the same and opposite direction have the same ratio.
3.
The
slope of a line is given by the ratio,
vertical component / horizontal component .
SECTION D: AN EQUATION OF A
LINE
1. The equation of a line that is not vertical has the form: y = i + sx, where i stands for the
y-intercept and s is the slope of the line.
2.
Another
way to describe the slope is to use the tangent ratio:
slope = tan a = vertical component / horizontal component
1.
You
can solve equations of the form a + bx = c + dx by drawing diagrams, by using
number lines, and by performing an operation (adding, subtracting,
multiplying, and/or dividing) on each side of the equation.
1.
You
can find the intersection point of two lines (for instance, y = - 3 - 2x and y
= 1+3x) by setting the lines
equal to one another and solving the equation –3 – 2x = 1 +
3x .