Question

Randolph is trying to find the equation of a line parallel to y = x − 6 in slope-intercept form that passes through the point (−1, 5). Which of the following equations will he use?
y − 5 = 1/4 (x − (−1))

y − (−1) = 1/4 (x − 5)

y − 5 = −4(x − (−1))

y − (−1) = −4(x − 5)

Answer 1

Here, Equation of a Line = y = x - 6
Line which is parallel, must have similar slope i.e, 1

Now, Coordinates are (-1, 5)
We know, principle equation, y - y1 = m(x - x1)
y - 5 = 1 (x + 1)

[ Please check your options, it is none of them ]

y - 5 = x + 1
y = x + 6

Hope this helps!

Answer 2

An equation of a line parallel to y=x-6, must have the same slope.

In this equation:
y=mx+b                        (slope-intercept form)
m is the slope:

The slope of the equation y=x-6 is m=1  (the number beside "x").

Now we have a point (-1,5) and the slope m=1.

Point-slope form of a line:
y-y₀=m(x-x₀)
so:
y-5=1(x+1)

answer: the equation of the line in point-slope form is :
y-5=1(x+1)

And the eqution of this line in slope-intercept form is:
y=x+6

y-5=(x+1)
y=x+1+5
y=x+6