Question

Write an equation in slope-intercept form for the line passing through the following pair of points: (2, -6), -4, 3).

Answer 1

The equation in slope intercept form is
`y=-(3)/(2) x-3`

Step-by-step explanation:

The given pair of points are
`(2,-6)` and
`(-4,3)`

The slope can be determined using the formula,

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Substituting the points
`(2,-6)` and
`(-4,3)` in the slope formula, we have,

`m=(3+6)/(-4-2)`

`m=(9)/(-6)`

`m=-(3)/(2)`

The equation in slope intercept form can be determined using the formula,

`y-y_1=m(x-x_1)`

Substituting
`m=-(3)/(2)` and the point
`(2,-6)` in the above formula, we get,

`y+6=-(3)/(2) (x-2)`

`y+6=-(3)/(2) x+3`

`y=-(3)/(2) x+3-6`

`y=-(3)/(2) x-3`

Thus, the equation in slope intercept form is
`y=-(3)/(2) x-3`