Question

Applying Slope-Intercept Form
The instructor had saved $3,500 and rents an apartment for $275 monthly. He believes the point (6, 1850) would be on the equation of the line. Is he correct? Explain how to check if a point is on a line.

Answer 1

Write the line in slope–intercept form: y = mx + b. Here b = 3500 (initial savings) and the monthly change m = −275 (rent reduces savings), so the equation is
y = −275x + 3500.

To check whether (6, 1850) is on the line, substitute x = 6 and see if you get y = 1850:
y = −275(6) + 3500 = −1650 + 3500 = 1850.

Since the computed y equals 1850, the point (6, 1850) is on the line.
(General check: plug the point’s x into the line and see whether the resulting y matches the point’s y.)