Final answer:
To find the equation of the line through (6,4) and (8,10), calculate the slope (m) as 3, then use one point to solve for the y-intercept (b), resulting in the equation y = 3x - 14.
Step-by-step explanation:
To find the equation of a line in the y=mx+b form that passes through the points (6,4) and (8,10), we first need to calculate the slope (m). The slope is the ratio of the rise (change in y) over the run (change in x) between two points. Using the given points, the slope is calculated as:
m = (y2 - y1) / (x2 - x1) = (10 - 4) / (8 - 6) = 6 / 2 = 3.
With the slope known, we can now determine the y-intercept (b) by substituting one of the points into the equation and solving for b:
y = mx + b
4 = 3(6) + b
b = 4 - 18
b = -14.
Therefore, the equation of the line is y = 3x - 14.