linear equations

Question

Passing through (2,3) and PARALLEL to y=x-4

Answer 1

through (2,3) parallel to y=x-4

y-3 = x-2

or

x-y = -1

the given line has slope =1 = the coefficient of the x term

any parallel line will also have the same slope

x has an implicit 1 as its coefficient

then plug in x=2 and y=3 to solve for b = y intercept

3 =2+b

b=1

y =x +1 is the equation in slope intercept form: y=mx+b, m=slope, b= intercept

x-y = -1 in standard form: ax+by = c, a=b=1, c =-1