2.2 Lines, 2.3 Lines, Finding the Equation of a Line

Finding the Equation of a Line given the slope and a point

Example:  Find the equation of a line in slope intercept form given the slope of the line is 7 and the line passes through the point (2,-3)

Solution:

Use the point-slope formula of the line to start building the line.  m represents the slope of the line and (x_1,y_1) is a point on the line.

Point-slope formula: y-y_1 = m(x-x_1)

m=7 and  (2,-3)

Substitute the values into the formula.

 y-(-3) = 7(x-2)

Since the instructions ask to write the equation in slope intercept form (y=mx+b) we will simplify and write the equation with y by itself on one side.

 y-(-3) = 7(x-2)

 y+3 = 7x-14

 y+3-3 = 7x-14-3

 y = 7x-17

The equation of a line in slope intercept form with a slope of 7 and  passing through the point (2,-3) is y = 7x-17.

Example: Find the equation of the line.