Respuesta :
Answer:
The intercept of the given points is - [tex]\frac{41}{11}[/tex]
Step-by-step explanation:
Given points as :
( [tex]x_1[/tex] , [tex]y_1[/tex] ) = ( [tex]\frac{3}{2}[/tex] , - 7 )
( [tex]x_2[/tex] , [tex]y_2[/tex] ) = ( - 4 , 5 )
Now, slope of line using given points can be written as :
Slope = m = [tex]\dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
or. m = [tex]\dfrac{5 - ( - 7 )}{( - 4 ) - [tex]\frac{3}{2}[/tex]}[/tex]
or, m = [tex]\dfrac{12}{( - 4 ) - [tex]\frac{3}{2}[/tex]}[/tex]
or, m = [tex]\frac{12}{\frac{- 8 - 3}{2}}[/tex]
Or, m = [tex]\frac{12}{\frac{- 11}{2}}[/tex]
∴ m = [tex]\frac{-24}{11}[/tex]
So, The slope of the line using points = m = [tex]\frac{-24}{11}[/tex]
now, equation of line in slope intercept form can be written as
y - [tex]y_2[/tex] = m × ( x - [tex]x_2[/tex] )
or, y - 5 = [tex]\frac{-24}{11}[/tex] × ( x - ( - 4 ) )
or, y - 5 = [tex]\frac{-24}{11}[/tex] × ( 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 = [tex]\frac{-24}{11}[/tex] x - [tex]\frac{41}{11}[/tex]
Now, comparing with slope intercept equation
I.e y = m x + c , where c is the intercept
So, The intercept of points is - [tex]\frac{41}{11}[/tex]
Hence The intercept of the given points is - [tex]\frac{41}{11}[/tex] Answer
