Final answer:
The line through the points (2,13) and (8,37) has a y-intercept of 5. This is found by first calculating the slope of the line and then using one of the points and the slope to solve for the y-intercept in the slope-intercept form of the line equation.
Step-by-step explanation:
To find the y-intercept of the line that passes through the points (2,13) and (8,37), we first need to find the slope of the line. The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
For the given points, this translates to:
m = (37 - 13) / (8 - 2) = 24 / 6 = 4
Now that we have the slope, we can use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Using one of the given points (2,13) to solve for b, we insert these into the equation:
13 = 4(2) + b
This gives us:
b = 13 - 8 = 5
Therefore, the y-intercept of the line is 5. This means the line will intersect the y-axis at the point (0,5).