Question

Gradients of a line and equations (link attached)

Answer 1

Gradient of Line ⊥ to AB = m = 3

B) y = 3x+11

Explanation:

A) Firstly, finding the slope of AB

Gradient =
`(rise)/(run)`

Gradient =
`(y2-y1)/(x2-x1)`

Gradient =
`(-2-2)/(7+5)`

Gradient =
`(-4)/(12)`

Gradient =
`(-1)/(3)`

Now, the line has a gradient of negative reciprocal to this one which is perpendicular to AB

So,

Gradient of Line ⊥ to AB = m = 3

B) Equation of line ⊥ to AB:

Gradient = m = 3

Now, Point = (x,y) = (-2,5)

So, x = -2, y = 5

Putting this in slope-intercept form to get b

=>
`y = mx+b`

=> 5 = (3)(-2) + b

=> 5+6 = b

=> b = 11

Now, Putting m and b in the slope intercept form to get the required equation:

=>
`y = mx+b`

=> y = 3x+11