
ALGEBRA
 solved problems 






Graphing
linear equation, linear function (first degree polynomial)

The linear function
f
(x)
= mx + c


The
linear function we also write as 
y
= a_{1}x + a_{0}
or y
= a_{1}(x

x_{0})
or y
 y_{0}
= a_{1}x,
where y_{0}
= a_{0} 
To find
the zero or the xintercept
of the linear function set y
= 0 and
solve the equation for x,
i.e., 
y
= 0 =>
0 = a_{1}x + a_{0} 


98. 
Find the equation of the line that passes through the
origin and the point
A(3,
2).


Translate the line in the direction of the xaxis
by x_{0} =

3, then find its equation.

Solution:
Calculate
the slope m by
plugging the 
coordinates of the point A
into the equation y =
mx, 

By
plugging x_{0} =

3 into y
= a_{1}(x

x_{0}) 





Equations
of straight line 
The
pointslope form of a line


99. 
Find the equation of the line that is parallel with the line y
=  x
 2 and passes through the point


P_{1}( 2,
1) .

Solution: 



The two point form of
the equation of a line 

100. 
Find the equation of the line which passes through points P(2,
3) and Q(6,
1).


Solution:




Find the equation of the line that is perpendicular to
the line


and passes
through 

the point A(2,
5).

Solution:



Absolute
value functions

The
graph of the absolute
value function f
(x)
= 
x



102. 
Draw the graph of the absolute value function
f
(x)
= 
x
.




The
graph of the absolute value of a linear
function f
(x) =
 ax+
b 


103. 
Draw the graph of the absolute value function
f
(x)
= 
ax + b
.




Simultaneous
linear equations

System of two linear equations in
two unknowns (variables)

Solving
systems of equations  substitution and comparison method


104. 
Solve the system of
equations.


Solution: 



105. 
Solve the system of
equations using comparison method.


Solution: 



Addition or elimination method


106. 
Solve the system of
equations using elimination method.


Solution: 












Solved
problems contents 


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