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ALGEBRA
- solved problems |
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Graphing
linear equation, linear function (first degree polynomial)
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The linear function
f
(x)
= mx + c
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The
linear function we also write as |
y
= a1x + a0
or y
= a1(x
-
x0)
or y
- y0
= a1x,
where y0
= a0 |
To find
the zero or the x-intercept
of the linear function set y
= 0 and
solve the equation for x,
i.e., |
y
= 0 =>
0 = a1x + a0 |
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98. |
Find the equation of the line that passes through the
origin and the point
A(-3,
2).
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Translate the line in the direction of the x-axis
by x0 =
-
3, then find its equation.
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Solution:
Calculate
the slope m by
plugging the |
coordinates of the point A
into the equation y =
mx, |
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By
plugging x0 =
-
3 into y
= a1(x
-
x0) |
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Equations
of straight line |
The
point-slope form of a line
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99. |
Find the equation of the line that is parallel with the line y
= - x
- 2 and passes through the point
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P1( 2,
1) .
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Solution: |
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The two point form of
the equation of a line |
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100. |
Find the equation of the line which passes through points P(-2,
3) and Q(6,
-1).
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Solution:
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Find the equation of the line that is perpendicular to
the line
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and passes
through |
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the point A(-2,
5).
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Solution:
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Absolute
value functions
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The
graph of the absolute
value function f
(x)
= |
x
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102. |
Draw the graph of the absolute value function
f
(x)
= |
x
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The
graph of the absolute value of a linear
function f
(x) =
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b |
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103. |
Draw the graph of the absolute value function
f
(x)
= |
ax + b
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Simultaneous
linear equations
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System of two linear equations in
two unknowns (variables)
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Solving
systems of equations - substitution and comparison method
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104. |
Solve the system of
equations.
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Solution: |
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105. |
Solve the system of
equations using comparison method.
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Solution: |
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Addition or elimination method
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106. |
Solve the system of
equations using elimination method.
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Solution: |
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Solved
problems contents |
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