using the
elimination method
to solve a linear equation
using the substitution method to
solve a linear equation:
there are 3 versions of the slope formula:
1. Slope intercept: y=mx+b
2. Point slope: y-y1=m(x-x1)
3. Standard: Ax+By=C
the point at which
two lines cross
a set of 2 or more linear
equations that are considered
at the same time
point of intersection
Chapter 3,4 and 5
Linear Systems
in the formula
y=mx+b, m is the slope
of the line, x is the variable
and b is the y-intercept
to rearrange an
equation from
standard from
into linear slope-intercept
form:
to solve a linear
equation involving
fractions:
to solve for the equation -6=x/5,
you will first need to get x by itself by cancelling out
the 5 in the denominator of the fraction by multiplying.
Next on the left side you multiply 5x(-6) which is -30,
therefore, x=-30
Adjacent
the side that forms one of the
angle being considered, but is
not the hypotenuse. The adjacent
side in triangle is highlighted green
opposite operations:
-opposite operations are
operations that "undo" each other
-addition and subtraction are
opposite operations
-multiplication & division are
opposite operations
Linear Equations
horizontal & vertical lines:
- a horizontal line has a slope of 0
- a vertical line has a slope that is undefined
calculating the slope
for the given equation:
the formula for finding the slope
in a graph is rise/run
rise=2
run=4
rise/run = 2/4
therefore, the slope in this is graph is 0.5
a coefficient is a number
that is multiplied by a variable
-in y=3x, the coefficient of x
is 3
linear relations is a relation
between two variables as
a straight line when graphed
the rate of change
is represented by the
sloe of the line
Linear Relations
the tangent is
the length of the opposite
side, divided by the length of
the adjacent side
in any right riangle,
the cosine of an angle
is the length of the
adjacent, divided by the
length of the hypotenuse
Tangent
Sine
the sine of an
angle is the length
of the opposite, divided by
the length of the hypotenuse
Cosine
Opposite side
the side that does not form one of
the arms of the angle being considered. The
opposite side in this triangle is written in red
Grade 10 Mathematics
Chapter 2:
Right Triangle Trigonometry
Hypotenuse
the longest side of a
right angle triangle. In this image, the
hypotenuse is written in blue.
the opposite of the
right angle
Pythagorean Theroeom
to find the hypotenuse:
the Pythagorean theory states that in a right angle
triangle, the square of the hypotenuse is equal
to the sum of the squares of the legs
Useful when building structures
the square of the hypotenuse is equal to the sum
of the squares legs
for a right angle triangle with legs a, b. and hypotenuse.
c=a2+b2
