Processing Math: 91%

From Förberedande kurs i matematik 1

Let's write down the equation for a straight line as

y=kx+m

where k and m are constants which we shall determine.

Since the points 23  and 30  should lie on the line, they must also satisfy the equation of the line,

3=k2+m and 0=k3+m

If we take the difference between the equations, m disappears and we can work out the gradient k,

3−0=k2+m−k3+m 

3=−k

Substituting this into the equation 0=k3+m then gives us a value for m,

m=−3k=−3−3=9 

The equation of the line is thus y=−3x+9.

NOTE: To be completely certain that we have calculated correctly, we check that the points 23  and 30  satisfy the equation of the line:

xy=23 : LHS= 3 and RHS= −32+9=3

xy=30 : LHS= \displaystyle 0 and LHS= \displaystyle -3\centerdot 3+9=0