Question

The equation of a line is y=1/4x-2. What is the equation of the line that is parallel to the first line and passes through (4, –2)?

Answer 1

The equation of the line that is parallel to y=1/4x-2 and passes through the point (4, -2) is y = 1/4x - 3.

Step-by-step explanation:

To find the equation of a line that is parallel to another and passes through a given point, you need to use the same slope as the original line. The given equation y=1/4x-2 has a slope of 1/4. Since parallel lines have identical slopes, the new line will also have a slope of 1/4.

Using the point-slope form of a line's equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through, we can substitute the given point (4, -2) into the equation. This gives us y - (-2) = 1/4(x - 4).

Simplifying the equation by distributing the slope and moving -2 to the other side, we get:

y = 1/4x - 1 -2

Combining like terms gives us the final equation:

y = 1/4x - 3

This is the equation of the line parallel to y=1/4x-2 and passing through the point (4, -2).

Answer 2

`\large\boxed{y=(1)/(4)x-3}`

Step-by-step explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

Parallel lines have the same slope. Therefore if given line is

`y=(1)/(4)x+2`

then the slope of our line is
`m=(1)/(4)`.

We have the equation:

`y=(1)/(4)x+b`

The line passes through (4, -2). Put the coordinsted pf the point to the equation:

`-2=(1)/(4)(4)+b`

`-2=1+b` subtract 1 from both sides

`-3=b\to b=-3`

Finally:

`y=(1)/(4)x-3`