Question

Find an equation of the line L that passes through the point (−6, 8) and satisfies the given condition. (Let x be the independent variable and y be the dependent variable.) The x-intercept of L is 3

Answer 1

`y=-(8)/(9)x+(8)/(3)`

Or

`9y+8x-24=0`

Explanation:

The line passes through
`(-6,8)`

The x-intercept being 3 means the line also passes through
`(3,0)`.

We can use the formula,

`m=(y_2-y_1)/(x_2-x_1)`

The slope of the given line is
`m=(0-8)/(3--6)`

This simplifies to

`m=-(8)/(9)`.

`y-0=-(8)/(9)(x-3)`

This gives

`y=-(8)/(9)x+(8)/(3)`

This is the slope-intercept form.

When we multiply through by 9, we get,

`9y=-8x+24`

Or

`9y+8x-24=0`