The equation of a line that is parallel to (2y - x = 16) and passes through the point (-6, 1) is [tex](y - 1)=0.5(x+6)[/tex] and this can be determined by using the slope-intercept form of the line.
Given :
First, convert the given line in slope-intercept form that is in the form of (y = mx + c).
2y = x + 16
[tex]y = \dfrac{1}{2}x +16[/tex]
Comparing the above equation with slope-intercept form.
m = 0.5
c = 16
The line parallel to the line (y = 0.5x + 16) means the slope of that line is also equal to 0.5.
The equation of the line whose slope is m and passing through the point [tex](x_1,y_1)[/tex] is given by:
[tex](y-y_1) = m(x-x_1)[/tex]
Now, put the value of slope m and point [tex](x_1,y_1)[/tex] in the above equation.
[tex](y - 1)=0.5(x+6)[/tex]
So, the equation of a line that is parallel to (2y - x = 16) and passes through the point (-6, 1) is [tex](y - 1)=0.5(x+6)[/tex].
For more information, refer to the link given below:
https://brainly.com/question/21835898
