Questions: Find an equation of the line containing the given pair of points. (2,5) and (6,8)

Solution Steps

To find the slope \( m \) of the line passing through the points \( (2, 5) \) and \( (6, 8) \), we use the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 5}{6 - 2} = \frac{3}{4} = 0.75 \]

Next, we calculate the y-intercept \( b \) using the slope and one of the points. Using the point \( (2, 5) \):

\[ b = y_1 - m \cdot x_1 = 5 - 0.75 \cdot 2 = 5 - 1.5 = 3.5 \]

Now that we have both the slope and the y-intercept, we can write the equation of the line in slope-intercept form \( y = mx + b \):

\[ y = 0.75x + 3.5 \]

Final Answer