Question

In the xy-plane, line l is parallel to the line with equation 4x-y=1. If line l contains the point (0,2), which of the following is an equation of line l? A) 4x-y = -2 B) 4x-y = 2C) 4x+y= -2 D) 4x+y =2

Answer 1

`\text{The equation for line I is 4x - y = -2 ( Option A)}`

The equation for the second line is:

`4x\text{ - y = 1}`
`\text{The general equation of a line is y = mx + c}`

Where m = slope and c = Intercept

Let us rewrite the given equation in that form :

`\text{ y = 4x - 1}`

Comparing y = 4x - 1 with y = mx + c:

m = 4 and c = -1

Since line I is parallel to the given line, it means their slopes are equal. Therefore, the slope for line I is also m = 4

Line I contains the Point:

`(x_1,y_{1)\text{ = }}(0,\text{ 2)}`

The equation of a line can also be written in the form:

`y-y_1=m(x-x_{1\text{ }})`
`y\text{ - 2 = 4 (x - 0)}`
`y\text{ - 2 = 4x}`

By rearranging the above equation:

`4x\text{ - y = -2}`

The above is the equation for line I