Solutions to Slope Problems

Detailed solutions to the slope problems are provided.

Solution to Problem 1:
The slope m is given by
m = (y2 - y1) / (x2 - x1) = (8 - 0) / (3 - (-1)) = 2

Solution to Problem 2:
The slope m is given by
m = (y2 - y1) / (x2 - x1) = (4 - 0) / (2 - 2) = 4 / 0
Division by zero is not allowed in maths. Therefore the slope of the line defined by the points (2 , 0) and (2 , 4) is undefined. The line through the points (2 , 0) and (2 , 4) is perpendicular to the x axis.

Solution to Problem 3:
The slope m is given by
m = (y2 - y1) / (x2 - x1) = (4 - 4) / (- 9 - 7) = 0 / -16 = 0
The line defined by the points (7 , 4) and (-9 , 4) is parallel to the x axis and its slope is equal to zero.

Solution to Problem 4:
We first find the slope defined by the points A(2 , 3) and B(5 , 6).
m(AB) = (y2 - y1) / (x2 - x1) = (6 - 3) / (5 - 2) = 3 / 3 = 1
We next find the slope defined by the points B(5 , 6) and C(0 , -2).
m(BC) = (y2 - y1) / (x2 - x1) = (- 2 - 6) / (0 - 5) = -8 / -5 = 8 / 5
The two slopes are not equal therefore the points are not collinear.

Solution to Problem 5:
The equation of the given line is
- y = - 2 x + 4
Rewrite in slope intercept form.
y = 2 x - 4
The slope of the given line is 2. Two parallel lines have equal slopes. Therefore the slope of the line parallel to the given line is also equal to 2.

Solution to Problem 6:
The equation of the given line is
- 2 y = - 8 x + 9
Rewrite in slope intercept form.
y = 4 x - 9/2
The slope of the given line is 4. Two perpendicular lines have slopes m1 and m2 related by:
m1 m2 = -1
If we set m1 = 4 then m2, the slope of the line perpendicular to the given line, is equal to -1/4.

Solution to Problem 7:
We first find the slope of the line defined by points A and B
m(AB) = (y2 - y1) / (x2 - x1) = (1 - (-1)) / (2 - 0) = 1
We next find the slope of the line defined by points A and C
m(AC) = (3 - (-1)) / (- 4 - 0) = 4 / - 4 = -1
The product of the slopes m(AB) and m(AC) is equal to -1 and this means that the lines defined by A,B and A,C are perpendicular and therefore the triangle whose vertices are the points A, B and C is a right triangle.

Solution to Problem 8:
The given equation
-7y + 8x = 9
Rewrite the equation in slope intercept form.
- 7y = - 8x + 9
y = (8/7) x - 9/7
The slope of the given line is 8/7

Solution to Problem 9:
The given equation
y = 9
The given equation is a line parallel to the x axis therefore it slope is equal to 0.

Solution to Problem 10:
The given equation
x = - 5
The given equation is perpendicular to the x axis therefore it slope is undefined.

More math problems with detailed solutions in this site.