Question

Gradients of a line and equations (link attached)

Answer 1

Answer:

Gradient of Line ⊥ to AB  = m = 3

B) y = 3x+11

Step-by-step explanation:

A) Firstly, finding the slope of AB

Gradient = $\frac{rise}{run}$

Gradient = $\frac{y2-y1}{x2-x1}$

Gradient = $\frac{-2-2}{7+5}$

Gradient = $\frac{-4}{12}$

Gradient = $\frac{-1}{3}$

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