Question

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

Answer 1

Answer:

$\huge\boxed{y=-\dfrac{5}{2}x-1}$

Step-by-step explanation:

Parallel lines have the same slope.

The slope-intercept form of an equationo f a line:

$y=mx+b$

m - slope

b - y-intercept

We have the equation of the line in a standard form.

Convert to the slope-intercept form:

$5x+2y=12$               subtract 5x from both sides

$2y=-5x+12$          divide both sides by 2

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

The slope

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

Therefore we have:

$y=-\dfrac{5}{2}x+b$

Substitute the coordinates of the given point (-2, 4):

$4=-\dfrac{5}{2}(-2)+b$

$4=5+b$             subtract 5 from both sides

$-1=b\to b=-1$

Finally we have:

$y=-\dfrac{5}{2}x-1$