Final answer:
The equation of a line with an x-intercept of 5 and a y-intercept of 2 is y = (-2/5)x + 2, using the slope-intercept form y = mx + b.
Step-by-step explanation:
To find the equation of a line whose x-intercept is 5 and y-intercept is 2, we can use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The x-intercept is the point where the line crosses the x-axis (y=0), and the y-intercept is the point where the line crosses the y-axis (x=0).
The slope m can be calculated as the rise over the run. In this case, the rise is -2 (since the y-intercept is 2 and the value of y at the x-intercept is 0) and the run is 5 (the x-intercept). This makes the slope m = -2/5. Now, we simply substitute the slope and the y-intercept into the equation to get:
y = (-2/5)x + 2
This is the equation of the line with the given intercepts.