Final answer:
The value of f for a line with a slope of 7 that passes through (–4, f) and (–3,2) is -5.
Step-by-step explanation:
To find the value of f for a line with a slope of 7 that passes through the points (‑4, f) and (‑3,2), we can use the slope formula which states that the slope is equal to the change in y divided by the change in x (rise over run).
In this case, we know the slope (m) is 7, and the change in x (x2 – x1) is 1 since (x2 – x1) = (‑3 – (‑4)) = 1. We can set up the equation m = (y2 – y1) / (x2 – x1) which becomes 7 = (2 – f) / 1. Multiplying both sides by 1 yields 7 = 2 – f, and by rearranging, we find f = 2 – 7. Finally, f = ‑5.