Answer:
y=-2x+8
Explanation:
Given the line:
[tex]y=\frac{1}{2}x-1[/tex]
We want to find a line that is perpendicular to the line with an x-intercept of 4.
Note: Two lines are perpendicular if the product of their slopes is -1.
Comparing y=½x-1 to the slope-intercept form y=mx+b, its slope =1/2.
Therefore, the slope of the line perpendicular to it = -2.
Since the x-intercept is 4, we have the point (4,0) on the line.
Using the point slope form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-0=-2(x-4) \\ y=-2x+8 \end{gathered}[/tex]
Therefore, the required line is: y=-2x+8
