Answer:
The equation of line passing through points (1 , 4) and (3 , - 4) is y = - 4 x + 8
Step-by-step explanation:
Given as :
A line is passing through points
[tex]x_1[/tex] , [tex]y_1[/tex] = 1 , 4
[tex]x_2[/tex] , [tex]y_2[/tex] = 3 , - 4
Now, Equation of line in point-slope form is
y - [tex]y_1[/tex] = m × (x - [tex]x_1[/tex])
where m is the slope of line
∵ m = [tex]\dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
i.e m = [tex]\dfrac{ ( - 4 ) - 4}{3 - 1}[/tex]
Or, m = [tex]\dfrac{ - 8}{2}[/tex]
Or, m = - 4
So, The slope of line = m = - 4
∵, equation of line can be written as
y - [tex]y_1[/tex] = m × (x - [tex]x_1[/tex])
So, Putting the value of slope, m and points ( [tex]x_1[/tex] , [tex]y_1[/tex] )
i.e y - 4 = ( - 4 ) × ( x - 1 )
Or, y - 4 = ( - 4 ) × x + 4
Or, y - 4 = - 4 x + 4
Or, y = - 4 x + 4 + 4
∴ y = - 4 x + 8
So, The equation of line y = - 4 x + 8
Hence, The equation of line passing through points (1 , 4) and (3 , - 4) is y = - 4 x + 8 Answer
