Question

Write an equation in standard form passing through the given line and parallel to the given line

Answer 1

Answer:

x + y = -2

Step-by-step explanation:

The given equation is y = -x - 5 and is of the form y = mx + c

Comparing y = -x - 5 with y = mx + c

the slope, m = -1

Two parallel lines always have equal slope

The line parallel to y = -x - 5 will also have a slope, m = -1

The line passes through the point (-1, -1)

The point-slope form of the equation of a line is:

`y-y_1=m(x-x_1)`

Substitute x₁ = -1, y₁ = -1, m = -1 into the point-slope equation above

`\begin{gathered} y-(-1)\text{ = -1(x-(-1))} \\ y+1\text{ = -1(x+1)} \\ y\text{ + 1 = -x - 1} \\ y\text{ = -x - 1 - 1} \\ y\text{ = -x - 2} \\ x\text{ +y = -2} \end{gathered}`

The equation passing through (-1, -1) and passing through y=-x-5 is:

x + y = -2