Question

The points (2,3) and (5,9) are on a line. What is the equation of the line?​

Answer 1

• The equation of the line is:
  `y=2x-1`

Explanation:

Given

• Two points on same line: (2, 3) and (5, 9)

To find

• The equation of the line

Solution

Find the slope of the line by formula:

• 
  `m=\cfrac{y_2-y_1}{x_2-x_1}`

Substitute and calculate:

• 
  `m=\cfrac{9-3}{5-2} =\cfrac{6}{3}=2`

Use point-slope equation to determine the line:

• 
  `y-y_1=m(x-x_1)`

Substitute and find:

• 
  `y-3=2(x-2)`
• 
  `y-3=2x-4`
• 
  `y=2x-4+3`
• 
  `y=2x-1`