What is an equation of the line that passes through the point (3, -3) and is parallel to the line x+3y=18?

Question

asked Apr 25, 2024 87.5k views

1 Answer

Brian Schermerhorn · Answer 1 · 2024-04-29T11:36:29+0000

Answer:

y=-(1)/(3)x-2

Explanation:

Linear equations are typically written slope-intercept form:

y = mx + b where m is the slope and b is the y-intercept

We're given this equation: x+3y=18

Rearrange into slope-intercept form:

$x+3y=18\\3y=18-x$

$y=6-(1)/(3)x\\y=-(1)/(3)x+6$

The slope of the line is
-(1)/(3) . A parallel line would have the same slope. Let's plug this into y = mx + b:

y=-(1)/(3)x+b

Now, plug in the given point:

$y=-(1)/(3)x+b\\\\-3=-(1)/(3)(3)+b\\\\-3=-1+b\\b = -2$

Therefore, the y-intercept is -2. Plug this back into the equation:

$y=-(1)/(3)x+b\\\\y=-(1)/(3)x-2$