Question

A line is represented by y=-2x+4. What would be the slope intercept form of a perpendicular line that goes

through (8,-3)?

Answer 1

`\displaystyle y=(1)/(2)x-7`

Explanation:

Perpendicular Lines

Two lines of slopes m1 and m2 are perpendicular if their slopes meet the condition:

`m_1\cdot m_2=-1\qquad \qquad [1]`

The slope-intercept form of a line with slope m and y-intercept of b is:

`y=mx+b`

The point-slope form of a line with slope m that passes through the point (h,k) is:

`y-k=m(x-h)`

We are given the line

`y=-2x+4`

From which we can know the value of the slope is m1=-2

The slope of the required line m2 can be calculated from [1]

`\displaystyle m_2=-(1)/(m_1)=-(1)/(-2)=(1)/(2)`

Now we know the slope and the point (8,-3) through which our line goes, thus:

`\displaystyle y-(-3)=(1)/(2)(x-8)`

To find the slope-intercept form, operate:

`\displaystyle y+3=(1)/(2)x-(1)/(2)\cdot 8`

`\displaystyle y=(1)/(2)x-4-3`

`\mathbf{\displaystyle y=(1)/(2)x-7}`