Question

Determine the slope-intercept form of the equation of the line parallel to y = x + 11 that passes through the point (–6, 2).

y=____x+_____

Answer 1

y=1x+8

Explanation:

Let's start with the general slope-intercept equation of a line, which is defined as:

(y-b)=m*(x-a), where:

(a,b) is a point belonging to the line, and, m is the line's slope.

The equation for the given line is:

y=x+11, which can be re-written as:

(y-11)=1(x-0)

This means that the slope of this line is m=1, and that a point belonging to the line is (0,11).

Since parallel lines are defined as lines with the same slope, then for the second line, we need to establish m=1.

Becuase the point (-6,2) is a point belonging to the second line, then we can express the general equation (y-b)=m*(x-a) as:

(y-2)=1(x-(-6)) which we can re-write as:

y=1(x-(-6))+2

y=1x+6+2

y=1x+8

In conclusion, the equation of a line that passes through the point (-6,2) and is parallel to the given line, can be described by the following equation in its slope-intercept form: y=1x+8.

Answer 2

Line parallel to y=x+11 so slopes are equal then
y= x+b
Passing through the point C (-6;2) then C belongs to this line
yc=xc+b
b= 6+2
b= 8
So y intercept is equal to 8