Question

Choose the equation of the line parallel to the line that passes x-2 that passes through the point (0,4). A y=x+4 C y=x+2 B y = 4x-2 D y = 2x + 4 c1

Answer 1

You have to find the equation of a line that is parallel to the line:

`y=x-2`

And passes through the point (0,4)

Two lines that are parallel have the same slope, in this exercise, in the equation of the line parallel to the one we have to determine we can see that the x-term is "alone". The slope of the line is the coefficient that multiplies the x-term, this value is not written, but the x-term is, in reality, being multiplied by "1", which represents the slope of the line.

So, the slope of the line we are looking for is m=1

Now that we know the slope of the line, using the point-slope form, you can determine the equation of the line:

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

Where

m represents the slope of the line

(x₁,y₁) represents one point of the line

Replace the expression with m=1 and (x₁,y₁)=(0,4)

`\begin{gathered} y-4=1(x-0) \\ y-4=1\cdot x \\ y-4=x \end{gathered}`

Pass "-4" to the right side of the expression by applying the opposite operation to both sides of the equal sign:

`\begin{gathered} y-4+4=x+4 \\ y=x+4 \end{gathered}`

The equation of the line, that is parallel to y=x-2 and passes through the point (0,4) is:

`A)\text{ y=x+4}`