Final answer:
The line that joins the points (2,5) and (-1,3) has a slope of 2/3. Using the point-slope form of the line and converting to slope-intercept form, the equation of the line is y = (2/3)x + (11/3).
Step-by-step explanation:
To find the function representing the line joining the points (2,5) and (-1,3), you first need to calculate the slope (m) of the line. The slope can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
For the points (2,5) and (-1,3), the slope calculation would be:
m = (3 - 5) / (-1 - 2) = (-2) / (-3) = 2/3.
Now that we have the slope, we can use the point-slope form of the line which is y - y1 = m(x - x1). Using point (2,5), the equation becomes:
y - 5 = (2/3)(x - 2).
To write it in slope-intercept form, which is y = mx + b, we simplify:
y = (2/3)x - (4/3) + 5,
y = (2/3)x + (11/3).
This is the equation of the line joining the points (2,5) and (-1,3).