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 P1(x1 , y1) and P2(x2, y2), its slope is given by:
m = (y2 - y1) / (x2 - x1)
with x2 not equal to x1.
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(x1 , y1) with slope m is given by
y - y1 = m(x - x1)
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 m1 and m2 are such that
m1 × m2 = - 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