Question

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

Answer 1

Answer:

The intercept of the given points is -  $\frac{41}{11}$

Step-by-step explanation:

Given points as :

( $x_1$ , $y_1$ ) = ( $\frac{3}{2}$ , - 7 )

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

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

Slope = m = $\dfrac{y_2 - y_1}{x_2 - x_1}$

or. m = $\dfrac{5 - ( - 7 )}{( - 4 ) - [tex]\frac{3}{2}$}[/tex]

or, m = $\dfrac{12}{( - 4 ) - [tex]\frac{3}{2}$}[/tex]

or, m = $\frac{12}{\frac{- 8 - 3}{2}}$

Or, m =  $\frac{12}{\frac{- 11}{2}}$

∴   m = $\frac{-24}{11}$

So, The slope of the line using points = m = $\frac{-24}{11}$

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

y - $y_2$ = m × ( x - $x_2$ )

or, y - 5 =  $\frac{-24}{11}$ × ( x - ( - 4 ) )

or, y - 5 =  $\frac{-24}{11}$ × ( 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 = $\frac{-24}{11}$ x -  $\frac{41}{11}$

Now, comparing with slope intercept equation

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

So, The intercept of points is  -  $\frac{41}{11}$

Hence The intercept of the given points is -  $\frac{41}{11}$ Answer