Answer:
The equation of line in slope intercept from can be written as:
[tex]y=-x[/tex]
where slope = -1 and y-intercept = 0
Step-by-step explanation:
To find the equation of line with point (4,-4) and parallel to line [tex]y=-x-4[/tex].
Solution:
The slope-intercept equation of the line is given as :
[tex]y=mx+b[/tex]
where [tex]m[/tex] represents slope of line and [tex]b[/tex] represent y-intercept.
The equation of the parallel line given is [tex]y=-x-4[/tex].
From the equation we can determine the slope of the line by comparing it with general equation.
Thus, slope of the given line is = -1 (co-efficient of [tex]x[/tex] )
Since the line is parallel to the given line, so the equation of line to be found out will have slope =-1 ( Parallel lines have same slopes)
Using point (4,-4) to write the point slope of the equation of line.
[tex]y-(-4)=-1(x-4)[/tex] [ As [tex]y-y_1=m(x-x_1)[/tex] ]
Simplifying by using distribution.
[tex]y+4=-x+4[/tex]
Subtracting both sides by [tex]4[/tex] to solve for [tex]y[/tex].
[tex]y+4-4=-x+4-4[/tex]
[tex]y=-x[/tex]
Thus, the equation of line in slope intercept from can be written as:
[tex]y=-x[/tex]
where slope = -1 and y-intercept = 0
