Finding Line Equations

Finding the equation of a line given a point and slope

 

Is there a line that goes through the point (-3,5) with the slope 2/3?

 

The information we have is:

 

- Slope

- X and Y values

 

This means we can come up with a formula that looks like this.

 

Y = 2/3x + b

5 = 2/3(-3) + b

 

The unknown value is b.

 

To find b we need to solve the equation using our knowledge of algebra.

 

5 = 2/3(-3) + b

5 + 5 = -2 + 2 + b

10 = b

 

Therefore the equation of the line with a slope of 3/5 that goes through the point

(-3,2) is:

 

y = 2/3x + 10

 

Practice:

 

Find the equation of a line that goes through (2, -5)  with a slope of -3/4.

 

Answer: y = -3/4x – (7/2)

 

Find the equation of a line that goes through (0,11) with a slope of 5/7.

 

Answer: y = 5/7x + 11

 

Find the equation of a line that goes through (-2,0) with a slope of -9.

 

Answer: y = -9x – 18