What is an equation of the line that passes through the point (−3,−4) and is parallel to the line x+y=6?

Answer 1

Isolate variable y to get your equation into slope intercept form y=mx+b where m is the slope

x+y=6 subtract x from both sides

-x -x

------------

y=-x+6 or y=-1x+6 *use imaginary variable 1 when there is no value in front of the variable (letter)

Now, your slope is the number (coefficient) in front of the variable x which is m=-1

slope m=-1 and we are given a point (-3,-4) =(x,y) Therefore we can use x=-3 and y=-4

Parallel lines have the same exact slope!!!!

so plug in the same exact slope as the first equation for the new line m=-1, & the given point (x,y)=(-3,-4) which implies that ....

x=-3, and y=-4 into slope intercept form y=mx+b

-4=(-1)(-3)+b simplify and solve for b

- 4= 3 + b multiply (-1)(-3)

-3 -3 subtract 3 from both sides of equation

------------------------

-7 = b 7= b is the y-intercept

rewrite y=mx+b by replacing m and b with the values

y=-1x + (-7) or y= -1x-7

Answer 2

Lines that are parallel have the same slope. Since the line we are looking for is parallel to x + y = 6, then we need to know the slope of x + y = 6. To determine the slope, put it in slope-intercept form (y = mx + b):

x + y = 6

Subtract "x" from both sides to get:

y = -x + 6

The coefficient in front of the "x" is the slope. Notice there is not a number but you can always put a "1" in front of any variable without changing it, so the slope is "-1"

Therefore the slope of the line we are seeking is "-1". We now have a point (-3, -4) and a slope "-1" so we can use the point-slope form of a line:

y - y₁ = m(x - x₁) where the point is (x₁, y₁) and the slope is "m"

Plug in the values to get:

y - -4 = -1(x - -3)

y + 4 = -1(x + 3)

You can use this as your answer since the question does no specify a particular form for the equation of the line.