Find the equations of the following lines
b. gradient -4 and passing through point (2, 1)
c. passing through the points (2, -1) and (4, 2)
d. passing through the points (1, -3) and (6, -5)
e. passing through the point (5, -2) and parallel to x + 5y + 15 = 0
f. passing through the point (1, 6) and parallel to x - 3y - 2 = 0
g. passing through the point (-1, -5) and perpendicular to 3x + y + 2 = 0

You need these two basic solutions and facts to find the equation of a line:

We can use this list to solve all the exercises:

b)

Use the first equation to get

c)

Use the second equation to get

d) same as c)

e) We derive the slope of the line by writing it as

So, the slope is -1/5. From here, it's the same as b)

f) same as e)

g) Again we find the slope as

so the slope is -3, and a perpendicular line has slope 1/3. From there, it's the same as b).

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.

1

step-by-step explanation:

it's the only multiple of both and the least