Question

write an equation in slope intercept form of the line that passes through the points and is parallel to the given equation
(2,-2); y=-x-2

a)y=-x-2x
b)y=2x
c)y=1/2x
d)y=-x

Answer 1

Answer:

option d

Step-by-step explanation:

The slope of the line y=-x-2 is -1

i.e. m=-1

so the line parallel to it will have the same slope i.e. m=-1

We know that point slope form is

y-y₁ = (m)(x-x₁)                      ................(i)

putting the values in the equation (i)

y-(-2)=(-1)(x-2)

y+2=-x+2

y+2=-x+2

subtracting 2 from both sides

y +2 -2 = -x +2 -2

solving

y= -x

Answer 2

Answer:

(d) y = -x

Step-by-step explanation:

General equation : y = mx + c

Find gradient , m:

Given that it is parallel to y = -x - 2

⇒ gradient of y = -x - 2 is -1

Parallel equation shares the same gradient

⇒ m of the parallel line = -1

Find y-intercept, c:

y = -1x + c

Given that it passes through (2, -2)

-2 = -1(2) + c

-2 = -2 + c

c = 0

⇒ The y-intercept = 0

Find the equation:

y = mx + c

m = -1, c = 0

Therefore the equation is y = -x

Answer: (d) y = -x