Final answer:
The slope of the line passing through the points (4, 2) and (7, 6.5) is 1.5. The formula for the line is y = 1.5x - 4.
Step-by-step explanation:
To find the slope for a line passing through the two points (4, 2) and (7, 6.5), we can use the slope formula, which is m = (y2 - y1) / (x2 - x1). Applying this formula to the points given, we get:
m = (6.5 - 2) / (7 - 4) = 4.5 / 3 = 1.5
Therefore, the slope of the line through these points is 1.5. To write the equation of the line, we start with the point-slope form which is y - y1 = m(x - x1). Using the slope we found and point (4, 2), the equation becomes: y - 2 = 1.5(x - 4).
Simplifying this equation to get the slope-intercept form (y = mx + b), we multiply out the right side and add 2 to both sides to isolate y:
y = 1.5x - 6 + 2
y = 1.5x - 4
Thus, the formula for the line is y = 1.5x - 4.