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.
If a line passes through two distinct points P_{1}(x_{1} , y_{1}) and P_{2}(x_{2}, y_{2}), its slope is given by:
m = (y_{2} - y_{1}) / (x_{2} - x_{1})
with x_{2} not equal to x_{1}.
The general equation of straight line is given by:
A x + B y = C
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.An equation of a line through a point P(x_{1} , y_{1}) with slope m is given by
y - y_{1} = m(x - x_{1})
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 = C / B.
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 m_{1} and m_{2} are such that
m_{1} × m_{2} = - 1
Question 1
Find the slope of a line passing through the points
Question 2
Find the equation of the line that passes through the point (-2 , 5) and has a slope of -4.
Solution to Question 2
Question 3
Find the equation of the line that passes through the points (0 , -1) and (3 , 5).
Solution to Question 3
Question 4
Find the slope of the line given by the equation
- 2 x + 4 y = 6
Question 5
Find an equation of the line that passes through the point (-2 , 3) and is parallel to the line 4 x + 4 y = 8
Solution to Question 5
Question 6
Find an equation of the line that passes through the point (0 , - 3) and is perpendicular to the line - x + y = 2.
Solution to Question 6
Matched Question 1
Find the slope of a line passing through the points
Matched Question 2
line that passes through the point (3 , 0) and has a slope of - 1.
Matched Question 3
Find the equation of the line that passes through the points (2 , 0) and (3 , 3).
Matched Question 4
Find the slope of the line given by the equation
x - 3 y = - 9
Matched Question 5
Find an equation of the line that passes through the point (-1 , 0) and is parallel to the line - 2 x + 2 y = 8.
Matched Question 6
Find an equation of the line that passes through the point (-2 , 1) and is perpendicular to the line x + 2 y = -2.
Matched Question 1
1) undefined
2) - 1 / 2
3) 0
Matched Question 2
y = - x + 3
Matched Question 3
y = 3 x - 6
Matched Question 4
slope = 1 / 3
Matched Question 5
y = x + 1
Matched Question 6
y = 2 x + 5