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Write an equation for the line in slope-intercept form.
Passing through (4,3)and parrallel to the line whose equation is y = -1/6x + 4.
1)The equation to a line in slope and y-intercept form is given by
y = (m)x +(b)
where m is the slope and b is the y-intercept
2)The line Passing through (4,3)and parrallel to the line whose equation is
y = -1/6x + 4.
Any line parallel to the given line y = (-1/6)x + 4. will be of the form}
y = (-1/6)x +k ----(*)
Now P(4,3) is a point on our line
Therefore putting x=4 and y = 3 in (*)
3= (-1/6)X(4) +k
Multiplying through out by 6
18 = -4 +6k
18+4 = 6k
22 = 6k
That is 6k = 22
k = 22/6 = 11/3
Putting k = 11/3 in (*)
the required line is y = (-1/6)x +(11)/3
which is a line with slope = (-1/6) and y-intercept =(11/3)
Verification: we check if (4,3) is a point on our answer line.
LHs = y = 3
RHS = (-1/6)x +(11)/3= (-1/6)X(4)+11/3 =(-2/3)+11/3
=(-2+11)/3 = 9/3= 3 = RHS
Therefore our equation is correct.
Note: Why did we take our equation in the form (*) with only the constant part different and the x and y part the same?
It is because,lines parallel implies slopes equal and hence the x any y part the same.In (*) actually for different values of k,we get different lines all of them parallel to the given line. But we want that parallel line which passes through (4,3). That is why we put x=4 and y=3 in (*) to get that particular k which will give our particular line. Got it!