Question

Find an equation of a line parallel to y=-x-2 and passes through the point (2,-2). Write answer form y=mx+b

Answer 1

Hi there!
The question here is asking us to write an equation of a line in slope-intercept form (y = mx + b) that goes through the point (2, -2) and is parallel to the line y = -x - 2. To do this, we need to take the slope of the original equation, which gives us -1. Now, we can use the point-slope formula - y - y₁ = m(x - x₁) - and plug in all the values and solve for y. We can set x₁ to be 2, y₁ to be -2, and m to be -1.
y - y₁ = m(x - x₁)
y + 2 = -1(x - 2)
y + 2 = -x + 2
-2 -2
y = -x
Therefore, the equation of the line that is parallel to the line represented by the equation y = -x - 2 and passes through the point (2, -2) is y = -x. Hope this helped and have a nice day!

Answer 2

To be parallel, this new line has to have the same slope as the other. To find the slope, we look at the number multiplying x.

-x means x is being multiplied by -1, so the slope, or m, is -1.

y = -x + b

Now, input the coordinate point and solve for b.

-2 = -1(2) + b
-2 = -2 + b
Add 2 to both sides.
0 = b

y = -x