Final answer:
To find the equation of the line through (5,1) and (-4,4), calculate the slope, which is -1/3. Then use the point-slope form with one point to create the equation, resulting in y = -1/3x + 8/3.
Step-by-step explanation:
To find an equation for the line that passes through the points (5,1) and (-4,4), we first need to determine the slope of the line.
The slope (m) is calculated by the difference in the y-values divided by the difference in the x-values, which is
(4 - 1) / (-4 - 5). This simplifies to 3 / -9, or -1/3.
With the slope and one of the points, we can use the point-slope form of a line, which is y - y1 = m(x - x1).
Using point (5,1), the equation becomes y - 1 = -1/3(x - 5).
To write this in the slope-intercept form (y = mx + b), we expand and simplify to get y = -1/3x + 5/3 + 1, and
finally, y = -1/3x + 8/3, which is the equation of the line passing through the two given points.