Question

What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4)?

y = – x – 1
y = – x + 5
y = x – 1
y = x + 5

Answer 1

I think the answer is y = -5/2x - 1, I'm doing the test right now. 

Answer 2

Answer: The equation of the line is
`y=-(5)/(2)x-1.`

Step-by-step explanation: We are given to find the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4).

The slope-intercept form of a straight line is

`y=mx+c,` where 'm' is the slope of the line and 'c' is the y-intercept.

From the given equation, we have

`5x+2y=12\\\\\Rightarrow 2y=-5x+12\\\\\Rightarrow y=-(5)/(2)x+6.`

So, the slope of the line is given by

`m=-(5)/(2).`

We know that the slopes of two parallel lines are equal.

Therefore, the equation of the line parallel to the line 5x + 2y = 12 and passing through the point (-2, 4) is given by

`y-4=m(x-(-2))\\\\\Rightarrow y-4=-(5)/(2)(x+2)\\\\\Rightarrow 2(y-4)=-5(x+2)\\\\\Rightarrow 2y-8=-5x-10\\\\\Rightarrow 2y=-5x-2\\\\\Rightarrow y=-(5)/(2)x-1.`

Thus, the required equation of the line is
`y=-(5)/(2)x-1.`