__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.

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