1. For each of the following pairs of points P₁P₂, find

a) slope of
b) distance
c) equation of the line passing through P₁ and P₂
d) midpoint of .

A.     P₁(0,1); P₂(2, -2)
B.     P₁(-5, -4); P₂(-1, 7)

2. Write the equation of the line with the given properties.

a) slope of and passing through (6,8)
b) passing through (4,1) and (8,6)
c) passing through (0,1) with a slope of
d) y-intercept of -2 and slope of

3. Write the equation of the line parallel to 2x + 3y - 36 = 0 and passing through (2, -3).

4. Write the equation of the line perpendicular to x - 2y - 4 = 0 and passing through (2, -3).

5. Find the linear function whose graph is parallel to the line segment containing (3, -1) & (4, 4) and has y-intercept of -2.

6. Find the linear function whose graph is perpendicular to the graph of 3x + 4y = 10and passes through (-2, 3).

7. What can you say about the formula for f(x) if f is linear and

a) 3f(x) = f(3x) and (1, -3) is on the graph of f
b) f(2x + 1) = f(2x) + 1
c) f(3) = 2 and f(0) = 5
d) f(x -5) = f(x) -5
e) f(4x + 3) = f(4x) and f(0) = 1
f) f(-1) = 1 and f(-2) = -1

 

ANSWERS Note: All equations for straight lines are written in general form.

1. A. a) m = b)    c) 3x + 2y - 2 = 0    d)
        B. a)     b)    c) 11x - 4y + 39 = 0     d)

2. a) 2x + 3y -36 = 0    b) 5x - 4y -16 = 0    c) x - 8y + 8 = 0    d) x - 2y - 4 = 0

3. 2x + 3y + 5 = 0

4. 2x + y - 1 = 0

5. y = 5x -2

6. 4x -3y + 17 = 0

7. a) y = -3x    b) m = 1; thus y = x + b    c) x + y - 5 = 0    d) m = 1; thus y = x + b   
        e) m = 0; thus y = 1    f) 2x - y + 3 = 0