Can you please help me understand this? Thanks

Question

Find the value of y so that the passing line through the two points has the given slope.

1. (2,y) (3,3) ;m=2

Answer 1

Two-point form of linear equation :

y - y1 = ( y2 - y1 ) * ( x - x1 ) / ( x2 - x1 )

Add y1 to both sides

y - y1 + y1 = ( y2 - y1 ) * ( x - x1 ) / ( x2 - x1 ) + y1

y = ( y2 - y1 ) * ( x - x1 ) / ( x2 - x1 ) + y1

Alope-intercept form of linear equation :

y = m x + b

In this case :

x1 = 2

y1 = y

x2 = 3

y2 = 3

m = ( y2 - y1 ) / ( x2 - x1 ) = 2

( 3 - y ) / ( 3 - 2 ) = 2

( 3 - y ) / 1 = 2

3 - y = 2 Subtract 2 to both sides

3 - y - 2 = 2 - 2

1 - y = 0 Add y to both sides

1 - y + y = 0 + y

1 = y

y = 1

Answer 2

just find the slope for the two points, set it equal to 2

(y-3)/(2-3) = 2 --- (y-3)/-1 = 2
y-3 = -2
y = 1