Question

which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Check all that apply. y = –x + 1 3x − 4y = −4 4x − 3y = −3 y – 2 = –(x – 4) y + 2 = (x + 4)

Answer 1

Explanation:

Given the equation 3x - 4y = 7

we have to find the equation which represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4, -2)

As parallel lines have same slope therefore we find the slope of given line

`3x-4y=7`

`4y=3x-7`

`y=(3)/(4)x-(7)/(4)`

Comparing above equation with general equation y=mx+c, where m is slope

⇒
`m=(3)/(4)`

`\text{The equation of line having slope }(3)/(4)\text{ and passing through the point (-4,-2) is}`

`y-y'=m(x-x')`

`y-(-2)=(3)/(4)(x-(-4))`

`y+2=(3)/(4)(x+4)`

`4y+8=3x+12`

`3x-4y=-4`

which is required equation.

Option 2 is correct.