Answer:
The y-intercept is ( 0 , 3 ) .
Step-by-step explanation:
Given as :
The points are
[tex]x_1[/tex] , [tex]y_1[/tex] = 2 , 5
[tex]x_2[/tex] , [tex]y_2[/tex] = 3 , 6
Let The slope of line with these points = m
So, Slope of line = [tex]\dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
i.e m = [tex]\dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
Or, m = [tex]\dfrac{6 - 5}{3 - 2}[/tex]
Or, m = [tex]\dfrac{1}{1}[/tex]
∴ m = 1
So, The slope = m = 1
Now, Equation of line with points [tex]x_1[/tex] , [tex]y_1[/tex] and slope m can be written as
y - tex]y_1[/tex] = m × ( x - tex]x_1[/tex] )
i.e y - 5 = 1 × ( x - 2 )
Or, y - 5 = x - 2
Or, y = x - 2 + 5
So, The equation of line is
y = x + 3
Again
For y - intercept
Put x = 0 in the line equation
∵ y = x + 3
Or, y = 0 + 3
∴ y = 3
So, The y - intercept = ( x , y ) = ( 0 , 3 )
Hence, The y-intercept is ( 0 , 3 ) . Answer
