Find the Line Through Points (2,2) and (9,16): Coordinate Geometry

Question

The line passes through the points (2,2),(9,16) (2,2),(9,16)

Video Solution

Step-by-Step Solution

To solve this problem, we'll calculate the slope of the line passing through the points (2,2)(2, 2) and (9,16)(9, 16).

  • Step 1: Identify the coordinates
  • Step 2: Apply the slope formula
  • Step 3: Simplify the expression

Let's proceed:

Step 1: The coordinates given are (x1,y1)=(2,2)(x_1, y_1) = (2, 2) and (x2,y2)=(9,16)(x_2, y_2) = (9, 16).

Step 2: The slope m m of a line through two points is given by:

m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1}

Substituting the coordinates into the formula, we have:

m=16292 m = \frac{16 - 2}{9 - 2}

Step 3: Simplify the expression:

m=147 m = \frac{14}{7}

m=2 m = 2

Therefore, the slope of the line is m=2\mathbf{m = 2}.

Answer

m=2 m=2