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 – 1y = – x + 5y = x – 1y = x + 5

Answer 1

The equation of the line parallel to 5x+2y=12 and passes through the point (-2, 4) is equal to y= -5/2x - 1

Answer 2

Answer:  The required equation of the line is $y=-\dfrac{5}{2}x-1.$

Step-by-step explanation:  We are given to find the equation of the line that is parallel to the following line and passes through the point (-2, 4) :

$5x+2y=12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that

the slope-intercept form of the equation of a straight line is given by

$y=mx+c,$

where m is the slope of the line.

From equation (i), we have

$5x+2y=12\\\\\Rightarrow 2y=-5x+12\\\\\Rightarrow y=-\dfrac{5}{2}x+6.$

So, the slope of line (i) is given by

$m=-\dfrac{5}{2}.$

We know that the slopes of two parallel lines are equal. So, the slope of the new line will be

$m=-\dfrac{5}{2}.$

Since the line passes through the point (-2, 4), so its equation will be

$y-4=m(x-(-2))\\\\\\\Rightarrow y-4=-\dfrac{5}{2}(x+2)\\\\\\\Rightarrow y-4=-\dfrac{5}{2}x-5+4\\\\\\\Rightarrow y=-\dfrac{5}{2}x-1.$

Thus, the required equation of the line is $y=-\dfrac{5}{2}x-1.$