Answer:
The parallel line cross the y-axis at point (0,6)
Step-by-step explanation:
we know that
If two lines are parallel, then their slopes are equal
step 1
Find the slope of the line that pass through the points (-2,2) and (2,0)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{0-2}{2+2}[/tex]
[tex]m=\frac{-2}{4}[/tex]
[tex]m=-\frac{1}{2}[/tex]
step 2
Find the equation of the line parallel to the given line and pass through the point (4,4)
The equation of a line in point slope form is
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{2}[/tex] --> remember that in parallel lines the slopes are the same
[tex]point\ (4,4)[/tex]
substitute
[tex]y-4=-\frac{1}{2}(x-4)[/tex]
Convert to slope intercept form
isolate the variable y
[tex]y-4=-\frac{1}{2}x+2[/tex]
[tex]y=-\frac{1}{2}x+2+4[/tex]
[tex]y=-\frac{1}{2}x+6[/tex]
step 3
Find the y-intercept
Remember that the y-intercept is the value of y when the value of x is equal to zero
so
For x=0
[tex]y=-\frac{1}{2}(0)+6[/tex]
[tex]y=6[/tex]
therefore
The parallel line cross the y-axis at point (0,6)
