Final answer:
To find y in the equation y−8=1/4(x−4), distribute the -1/4 across the parentheses and then isolate y to get y = (-1/4)x + 9, where -1/4 is the slope and 9 is the y-intercept.
Step-by-step explanation:
The equation given by the student is y−8=1/4(x−4) in the slope-intercept form, where the aim is to find the value of y. To convert this into the form y=mx+b, we first need to distribute the -1/4 across the parenthesis to both x and -4. This leads us to y - 8 = (-1/4)x + 1 (since -1/4 multiplied by -4 is 1). The next step is to add 8 to both sides to solve for y, giving us y = (-1/4)x + 9. Thus, m is the slope, which is -1/4, and b is the y-intercept, which is 9. From this, it can be stated that the line crosses the y-axis at the point (0, 9) and that for each unit increase in x, the value of y decreases by 1/4.