Homework Due Friday Feb 18

Follow along with the examples on the following pages in the RED BOOK and do the sums given


p. 239

Read c and d and then do the following problems:

1)

EXAMPLES: y = 4 is a horizontal line which crosses the y-axis at 4.  x = 2 is a vertical line which crosses the x-axis at 2.

Write an equation for the lines shown in c and d. 

2) Think of gradient as “Rise over run” – i.e. with each “step” a climber would take on the slope of a line, their gradient is the how high up they go divided by how far to the right they go in a single step.  For y = k (where k is a constant) the gradient is zero because for each step taken, the climber is going to the right but not going up at all. For x = k, we can see in d) that the gradient is undefined.  What does this mean in terms of a climber?  How high up is the climber going for every step to the right?

3) Read Example 5.2.1c.  Now draw a line with gradient -2 which goes through A(2,2).

p. 240

Read Example 5.2.1d in detail.  Try solving a-d yourself first, then look at the answers.

p. 241

1) Line 1 passes through the points A(-2,-1) and B(3,4).  Find the equation of a line which is parallel to Line 1 as passes through the origin (0,0).

2) Line 2 passes through the points A(-3, 2) and B(2,-2).  Find the equation of a line which is parallel to Line 2 and passes through the point A(1,1).

p. 244

1) Consider two points A(-3,1) and B(3, 1) which lie on a line.  Write the coordinates of any two other points which lie on this line.

2) A(-2,-1) and B(4, -5) lie on a line.  Write the coordinates of any two other points which lie on this line between A and B.

3) Does the origin lie on either of the lines given in 1) and 2)?  Show your work.

p. 245 Example 5.2.4 c

1) Write the equation of the line passing through A(2,3) and B(6, 2) in the forms y = mx + c and ax + by + d = 0

2) Write the equation of the line passing through A(-1, -2) and B(3, 8) in the forms y = mx + c and ax + by + d = 0

3) The equation of a particular line is y = 2x + 4.  Write this line in the form ax + by +d = 0

4) The equation of a line is y = -(3/5)x -2.  Write this line in the form ax +by + d = 0