Question

Where do (3/2,-7) and (-4,5) intercept

Answer 1

The intercept of the given points is -
`(41)/(11)`

Explanation:

Given points as :

(
`x_1` ,
`y_1` ) = (
`(3)/(2)` , - 7 )

(
`x_2` ,
`y_2` ) = ( - 4 , 5 )

Now, slope of line using given points can be written as :

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

or. m =
}[/tex]

or, m =
}[/tex]

or, m =
`(12)/((- 8 - 3)/(2))`

Or, m =
`(12)/((- 11)/(2))`

∴ m =
`(-24)/(11)`

So, The slope of the line using points = m =
`(-24)/(11)`

now, equation of line in slope intercept form can be written as

y -
`y_2` = m × ( x -
`x_2` )

or, y - 5 =
`(-24)/(11)` × ( x - ( - 4 ) )

or, y - 5 =
`(-24)/(11)` × ( x + 4 )

Or, 11 × ( y - 5 ) = - 24 × ( x + 4 )

Or, 11 y - 55 = - 24 x - 96

Or, 11 y = - 24 x - 96 + 55

Or, 11 y = - 24 x - 41

∴ y =
`(-24)/(11)` x -
`(41)/(11)`

Now, comparing with slope intercept equation

I.e y = m x + c , where c is the intercept

So, The intercept of points is -
`(41)/(11)`

Hence The intercept of the given points is -
`(41)/(11)` Answer