4. The straight line, L1, has equation y = x – 2.

Question

(a) Write down the y intercept of L1.
(1)
(b) Write down the gradient of L1.
(1)
The line L2 is perpendicular to L1 and passes through the point (3, 7).
(c) Write down the gradient of the line L2.
(1)
(d) Find the equation of L2. Give your answer in the form ax + by + d = 0 where a, b, d .

Answer 1

(a) The y-intercept of L1 is -2.

(b) The gradient of L1 is 1.

(c) Since L2 is perpendicular to L1, the gradient of L2 is the negative reciprocal of 1, which is -1.

(d) To find the equation of L2, we can use the point-slope form:

y - y1 = m(x - x1)

Where (x1, y1) is the point (3, 7) and m is the gradient of L2, which is -1.

Using the point (3, 7):

y - 7 = -1(x - 3)

Simplifying:

y - 7 = -x + 3

Rearranging the equation:

x + y - 10 = 0

So, the equation of L2 is x + y - 10 = 0.