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 = 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
 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 x-axis by x0 = - 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 x0 = - 3 into  y = a1(x - x0)
Equations of straight line
The point-slope 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
P1( 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:
 101
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