Explain how to write an equation for the line that contains the point (2, -3) and is parallel to the graph of x + 2y = 2

The equation of the line which is parallel to the given line and passing through the given point is x + 2y + 2 = 0

It is an endless 1-dimension figure that has no width.

Given

Line x + 2y = 2

Point (2, -3)

Equation of parallel line is given by ax + by + c = 0

But the line is parallel to the given line x + 2y -2 = 0 so the coefficients of x and y will be the same.

a = 1

b = 2

Then line becomes x + 2y + c = 0

The line is passing through the point (2, -3)

Then the equation of the line which is parallel to the given line and passing through the given point is x + 2y + 2 = 0

Thus, the equation of the line which is parallel to the given line and passing through the given point is x + 2y + 2 = 0

More about the straight-line link is given below.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.