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 =…

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asked Dec 5, 2023 29.9k views

1 Answer

Alessandro Gaballo · Answer 1 · 2023-12-11T04:30:00+0000

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

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