Question

For (-4,1), (4,6) What is the angle that the line toning the given points makes with the positive direction of the x-axis?

Answer 1

`32^@`

Explanation:

`•color(white)(x)tantheta=m`

`"where m is the slope and "theta" is the angle between "`
`"the line and the positive direction of the x-axis"`

`"calculate m using the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(-4,1)" and "(x_2,y_2)=(4,6)`

`rArrm=(6-1)/(4+4)=5/8`

`rArrtantheta=5/8`

`rArrtheta=tan^-1(5/8)=32^@`