Answer:
[tex]y = \frac{1}{3}x + 3[/tex]
Step-by-step explanation:
The slope of two parallel straight lines are the same.
Now, the slope of the line [tex]y = \frac{1}{2} x + 8[/tex] is [tex]\frac{1}{2}[/tex] as the straight line equation is in slope-intercept form.
Now, the equation of the straight line in slope-intercept form which is parallel to the above line is [tex]y = \frac{1}{2} x + c[/tex] ............. (1) , where c is any constant.
Now, point (-2,2) is on the line (1) {Given}
So, this point will satisfy the equation.
Hence, [tex]2 = \frac{1}{2} (- 2) + c[/tex]
⇒ c = 3.
Therefore, the equation of the required straight line is [tex]y = \frac{1}{3}x + 3[/tex] (Answer)
