Find the Line Through Points (3,7) and (6,14): Coordinate Geometry

Question

The line passes through the points (3,7),(6,14) (3,7),(6,14)

Video Solution

Step-by-Step Solution

To solve this problem, we'll calculate the slope of the line passing through the points (3,7) (3, 7) and (6,14) (6, 14) . The formula for the slope m m of a line through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by:

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

First, we identify our points as follows:
Point 1: (x1,y1)=(3,7)(x_1, y_1) = (3, 7)
Point 2: (x2,y2)=(6,14)(x_2, y_2) = (6, 14)

Next, apply the formula:
x1=3y1=7x2=6y2=14 x_1 = 3 \\ y_1 = 7 \\ x_2 = 6 \\ y_2 = 14 \\
Substitute into the slope formula:
m=14763=73 m = \frac{14 - 7}{6 - 3} = \frac{7}{3}

Therefore, the slope of the line is m=73=213 m = \frac{7}{3} = 2\frac{1}{3} .

The correct choice from the given options is: m=213 m=2\frac{1}{3} .

Answer

m=213 m=2\frac{1}{3}