Find an equation of the line containing the given pair of points (3,5)& (9,8)
Ok, if we know 2 points we can determine the slope as the difference of the y-values over the difference of the x-values. Thus if P=(3,5)& Q=(9,8)
m =(8-5)/(9-3)
Now if you know the slope and a point you can write the equation as:
y-y0=m(x-x0), or
y=mx +(-mx0+y0) which is the point-slope form for the line and (x0,y0) is either of the two points above.
Do you think you can finish the equation?
Sure, let's continue.
Using the slope we previously calculated:
m = (8-5)/(9-3) = 3/6 = 1/2
Now, let's choose one of the points, for example, P(3,5). We can substitute the values into the point-slope form:
y - y0 = m(x - x0)
Substituting in the values for P(3,5):
y - 5 = (1/2)(x - 3)
To simplify the equation, let's distribute the 1/2 to the terms in the brackets:
y - 5 = (1/2)x - (3/2)
Combining like terms:
y = (1/2)x - (3/2) + 5
y = (1/2)x + (7/2)
Therefore, the equation of the line containing the points (3,5) and (9,8) is y = (1/2)x + (7/2).