f (x) = m x + b.If we let y = f (x) then it looks like this:
y = m x + b.This is called the equation of a straight line because if we plot the points that satisfy this equation on a graph of y versus x then, as we will see below, the points all lie on a straight line.
y = m x + b,on this plane and show that the graph is a straight line. To do this we make the following table of values of y (that is, of the expression m x + b ) versus x:
Conclusion: The equation y = m x + b,where m and b are constants, is the equation of a straight line. m is called the slope and b is called the y intercept. This form of the equation is called the slope-intercept form. There are other possible forms; click here to see them. |
y_{1} = m x_{1} + b
y_{1} = m x_{1} + bSimilarly, take the second point, (x_{2}, y_{2}), and substitute it into the straight line equation, y = m x + b. This gives:
y_{2} = m x_{2} + b
y_{2} − y_{1} = m x_{2} − m x_{1},which, when solved for m, gives the same equation as in the other two methods, namely:
= −5.By inspection the y intercept is
b = 15.Substituting these two values for m and b into the straight line equation, y = m x + b, gives
y = −5 x + 15.
y = 2 x + 1.
Algebra Coach Exercises |