a = –5
Solution:
Given data: [tex]y=-\frac{1}{2}ax[/tex], [tex]m=\frac{5}{2}[/tex]
The standard equation of a line is y = mx + c.
In the line [tex]y=-\frac{1}{2}ax[/tex] can be written as [tex]y=-\frac{1}{2}ax+0[/tex].
The slope of the line [tex]y=-\frac{1}{2}ax+0[/tex] is [tex]m=\frac{-1}{2}a[/tex].
Given [tex]m=\frac{5}{2}[/tex].
Both are slopes of the line. So,we can equate the both slopes.
⇒ [tex]\frac{-1}{2}a=\frac{5}{2}[/tex]
⇒ [tex]a=\frac{5}{2}\times\frac{-2}{1}[/tex]
⇒ a = –5
Hence the value of a is –5.
