Question

write the equation of the line that passes through the points (6, 0) and (8, 7). put your answer in fully simplified point - slope form, unless it is a vertical or horizontal line.

Explanation:

Step1: Find the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1, y_1)=(6, 0)\) and \((x_2, y_2)=(8, 7)\), so \( m=\frac{7 - 0}{8 - 6}=\frac{7}{2} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((6, 0)\) (we could also use \((8, 7)\)). Substituting \( m = \frac{7}{2} \), \( x_1 = 6 \), and \( y_1 = 0 \) into the point - slope formula, we get \( y-0=\frac{7}{2}(x - 6) \), which simplifies to \( y=\frac{7}{2}(x - 6) \).

Answer:

\( y=\frac{7}{2}(x - 6) \)