Question

a line is drawn perpendicular to y=(1/2)x+6 and passes through the points (b,1) and (-3,2). what is the value of b

Answer 1

`{ \tt{y = (1)/(2) x + 6}} \\`

- If two lines areperpendicular, their gradients have a relation below;

`{ \tt{m_(1) * m _(2) = - 1 }} \\`

- Therefore, gradient for points (b, 1) and (-3, 2);

`{ \tt{ (1)/(2) * m _(2) = - 1}} \\ \\ { \tt{m = - 2}}`

- Therefore:

`{ \tt{ - 2 = (2 - 1)/( - 3 - b) }} \\ \\ { \tt{ - 2( - 3 - b) = 1}} \\ \\ { \tt{6 + 2b = 1}} \\ { \tt{2b = - 5}} \\ { \tt{b = - (5)/(2) }}`