The graph shows a line through the points -2,-2 and 2,0 . consider the line parallel to this line through the point 4,4 . where will the parallel line cross the y-axis (it's y-intercept) ?

Answer:The parallel line cross the y-axis at point (0,6)Step-by-step explanation:we know thatIf two lines are parallel, then their slopes are equalstep 1Find 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 2Find 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 formisolate 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 3Find the y-interceptRemember that the y-intercept is the value of y when the value of x is equal to zerosoFor x=0[tex]y=-\frac{1}{2}(0)+6[/tex][tex]y=6[/tex]thereforeThe parallel line cross the y-axis at point (0,6)