Question

question 18 of 25
what is the equation of the line containing the points (7, 3), (14, 6), and
(21, 9)?

a. ( y = \frac{3}{7}x )

b. ( y = \frac{1}{7}x )

c. ( y = x - 4 )

Explanation:

Step1: Calculate the slope

Using the formula for slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \), take the points \((7,3)\) and \((14,6)\).
\( m=\frac{6 - 3}{14 - 7}=\frac{3}{7} \).
Check with another pair, say \((14,6)\) and \((21,9)\): \( m=\frac{9 - 6}{21 - 14}=\frac{3}{7} \), so slope is consistent.

Step2: Use point - slope form

Using point - slope form \( y - y_1=m(x - x_1) \), take the point \((7,3)\) and \( m = \frac{3}{7} \).
\( y - 3=\frac{3}{7}(x - 7) \)
Expand: \( y - 3=\frac{3}{7}x-3 \)
Add 3 to both sides: \( y=\frac{3}{7}x \)

Answer:

A. \( y=\frac{3}{7}x \)