Final answer:
The y-intercept of the equation 8x + y = 39 is (0, 39), and the x-intercept is (4.875, 0) or as an improper fraction, 39/8 in simplest form.
Step-by-step explanation:
To find the x- and y-intercepts of the graph of the equation 8x + y = 39, we need to determine the points at which the graph crosses the x-axis and y-axis.
Y-intercept:
To find the y-intercept, set x to 0 and solve for y. Doing so, we get:
8(0) + y = 39
y = 39
Therefore, the y-intercept is the point (0, 39).
X-intercept:
To find the x-intercept, set y to 0 and solve for x. This gives us:
8x + 0 = 39
x = 39/8
x = 4.875
Thus, the x-intercept is the point (4.875, 0), which can also be expressed as the improper fraction 39/8 in simplest form.