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

Answer:
`y=-(5)/(2)x-1`

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

Write the equation of the given line in Slope-Intercept form by solving for "y":

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

You can observe that the slope of this line is:

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

Since the slopes of parallel lines are equal, then the slope of the other line is:

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

Now, substitute the slope and the point (-2, 4) into
`y=mx+b` and solve for "b":

`4=-(5)/(2)(-2)+b\\\\4=(10)/(2)+b\\\\4-5=b\\\\b=-1`

Then the equation of the line parallel to the given line is:

`y=-(5)/(2)x-1`