Question

What is the y-intercept of the line passing through the point (1, 4) with a slope of − 1 6 − 6 1 ​ ? A. 2 5 6 6 25 ​ B. 5 3 3 5 ​ C. − 1 3 − 3 1 ​ D. − 2 3 6 − 6 23 ​

Answer 1

The y-intercept of the line passing through the point (1, 4) with a slope of
`-(1)/(6)` is
`(25)/(6)`.

The correct answer is option a.
`(25)/(6)`

To determine the y-intercept of the line passing through the point (1, 4) with a slope of
`-(1)/(6)` , we can use the point-slope form of a linear equation,
`y-y_(1) =m(x-x_(1) )`,where
`(x_(1),y_(1) )` is the given point, and m is the slope.

Given the point (1, 4) and slope
`m=-(1)/(6)` the equation becomes
`y-4= -(1)/(6)(x-1)`. Now, we can simplify this equation to slope-intercept form
`(y=mx+b)`, where b is the y-intercept.

`y-4=-(1)/(6)x +(1)/(6)` ⟹
`y=-(1)/(6)x + (25)/(6)`

Comparing this equation with the slope-intercept form, we find that the y-intercept (b) is
`(25)/(6)`

Therefore, the correct option is: A.
`(25)/(6)`