Question

Find an equation for the line: through (–4, 6) and parallel to y = -3x + 4

Answer 1

NOTE: The equation of 2 parallel lines will always have the same slope.
Given y = -3x+4, this is written in slope intercept form (i.e y=mx+b, where m=slope,
b= y-intercept).
1. From the equation: y = -3x+4: slope(m)=-3.
The slope (m) of the parallel line is also m=-3.
2. Use the point-slope form: \[y-y _{1}=m(x-x _{1})\]
Slope (m)=-3 and given the point: (-4,6) from the point \[x _{1}=-4, y _{1}=6\]

equation: y-6= -3(x-(-4))
y-6 = -3(x+4)
y-6 = -3x-12 (solve for y by adding 6 to both sides)
y = -3x-6 (answer in slope-intercept form)

To write answer in Standard form (ax+by+c=0), where a is positive and all the coefficients are integers (not fractions or decimals)
we have
y-6 = -3x-12 (move x term to the left side: by adding 3x to both sides)
3x+y-6 = -12 (add 12 to both sides)
3x+y+6 = 0, in standard form

Answer 2

Any questions about this?

Answer 3

No, haha. Thanks!