Question

The equation of line L is 2x+y=3

Line M is parallel to line L and passes through
(1,−6)

Work out the equation of line M.
Give your answer in the form
y=ax+b

(3 marks)

Answer 1

To find the equation of line M which is parallel to line L and passes through (1, -6), we use the slope-intercept form of a line and substitute the given point to find the y-intercept.

Step-by-step explanation:

To find the equation of line M which is parallel to line L and passes through (1, -6), we first need to find the slope of line L. The given equation of line L is 2x + y = 3. To convert it into the form y = ax + b, we subtract 2x from both sides, giving us y = -2x + 3. The slope of line L is -2.

Since line M is parallel to line L, it will have the same slope. Therefore, the equation of line M can be written as y = -2x + b, where b is the y-intercept that we need to find.

Since line M passes through (1, -6), we can substitute x = 1 and y = -6 into the equation y = -2x + b. This gives us -6 = -2(1) + b. Solving for b, we get b = -4. Therefore, the equation of line M is y = -2x - 4.

Answer 2

y = -2x - 4

Step-by-step explanation:

We transform the line equation of L:

2x + y = 3 --(-2x)--> f(x) = y = -2x + 3

We now know that L intersects the y-axis at 3 and it has a slope of -2.

In order to construct a parallel line M, it needs to have an identical slope to L.

All we need to do now is to move one step from the given point (1,-6) towards 0 with the predetermined slope of -2, resulting in the point (0,-4).

Since we know slope and intersection with the y-axis (0,-4), we can construct the line equation:

f(x) = y = -2x - 4 for line M.