Final answer:
The equation of the line that passes through the point (8,3) with a slope of -¼ is y = -¼x + 5. This is found by using the point-slope form and simplifying it to the slope-intercept form.
Step-by-step explanation:
To find the equation of the line that passes through the point (8,3) and has a slope of -¼, you can use the point-slope form of a line which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, x1 = 8, y1 = 3, and the slope m = -¼. Plugging in these values, the equation becomes:
y - 3 = -¼(x - 8).
This equation can be further simplified to solve for y, which will give us the slope-intercept form of the equation:
y - 3 = -¼x + 2,
and then,
y = -¼x + 2 + 3,
y = -¼x + 5.
The final equation of the line is y = -¼x + 5.