Question on how to find the slopes and equations of lines. A review of the concepts of slope and equations of lines are presented followed by questions with detailed solutions.
Slopes and Equations of Lines
Slope of a Line:
If a line passes through two distinct points P1(x1 , y1) and P2(x2, y2), its slope is given by:
m = (y2 - y1) / (x2 - x1)
with x2 not equal to x1.
General Equation of a Straight line:
The general equation of straight line is given by:
A x + B y = C
where A, B and C are constants and A and B cannot be both zero.
An interactive exploration of the equations of lines of the form A x + B y = c is included.
Any straight line in a rectangular system has an equation of the form given above.
Slope intercept form of a Line:
The equation of a line with a defined slope m can also be written as follows:
y = m x + b
where m is the slope of the line and b is the y intercept of the graph of the line.
The above form is called the slope intercept form of a line. Further interactive tutorials on this form of lines are included.
Point-Slope form of a line:
An equation of a line through a point P(x1 , y1)
with slope m is given by
y - y1 = m(x - x1)
Vertical and Horizontal lines:
a - If we set A to zero in the general equation, we obtain an equation in y only of the form
B y = C
which gives y = C / B = k; k is a constant. This is a horizontal line with slope 0 and passes through all points with y coordinate equal to k.
b - If we set B to zero in the general equation, we obtain
A x = C
which gives x = C / A = h; h is constant. This is a vertical line with undefined slope and passes through all points with x coordinate equal to h.
Two non vertical lines are parallel if and only if their slopes are equal.
Two non vertical lines are perpendicular if and only if
their slopes m1 and m2 are such that
m1 × m2 = - 1
Questions with Solutions
Question 1 Find the slope of a line passing through the points