Question

State the equation of a line that is perpendicular to the equation y = -1/2 x + 3 and going through the point (7,-1).

Answer 1

`y=2x-15`

Explanation:

1. The equation of the line in the slope-intercept form is
`y=3-(x)/(2)`

2. The slope of the perpendicular line is negative inverse:
`m=2`

3. So, the equation of the perpendicular line is
`y=2x-a`

4. To find
`a`, the line should pass through the given point:
`-1=(2)(7)+a`

5. Thus,
`a=-15`

6. Therefore, the equation of the line is
`y=2x-15`

7. Answer:
`y=2x-15`