What is an equation of the line that passes through the point (4, -6) and is parallel to the line x + y = 4

The answer is: y = -x - 2

Step-by-step explanation:

Given point: (4, -6)

Given line: x + y = 4

A parallel line will have the same slope as the given line. Put the equation in the form y = mx + b to find the slope, m:

y = -x + 4 or y = -1x + 4, so the slope is m = -1

Use the point slope form of the equation, and substitute the slope and the given point:

y - y1 = m(x - x1)

y - (-6) = -1(x - 4)

y + 6 = -x + 4

y = -x - 2

Proof:

f(4) = -4 - 2

= -6, Giving point (4, -6)

Hope this Helps! Have an Awesome Day!!  :-)

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step-by-step explanation:

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so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!