Final answer:
The y-intercept of the line through the point (5,2) with a slope of 1 can be found by plugging these values into the slope-intercept equation y = mx + b, resulting in a y-intercept of -3.
Step-by-step explanation:
To find the y-intercept of a line that passes through the point (5,2) and has a slope of 1, you can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, we are given the slope m = 1 and a point (5, 2) that lies on the line. From the point (5, 2), we can plug these values into the slope-intercept equation to solve for b.
Using the given point (5, 2), the equation would be 2 = (1)(5) + b. We then solve for b by subtracting 5 from both sides to get b = -3. Therefore, the y-intercept is -3, which means the line crosses the y-axis at the point (0, -3).
This process utilizes algebraic techniques to determine the starting point of the line on the y-axis, which is crucial in plotting linear equations and understanding their graphs in more than 100 words.