Question

Byron's workout starts with a warm-up at home, and then he runs at 4 mi/h. After half an hour of running, he is 2 miles from home. What is an equation in point-slope form that represents Byron's distance from home, y, after x hours?

a) y - 2 = 4(x - 0.5)
b) y = 4x - 2
c) y - 2 = 4x
d) y = 4(x - 0.5)

Answer 1

The correct equation in point-slope form representing Byron's distance from home after x hours is y - 2 = 4(x - 0.5).

So, the correct answer is A.

Step-by-step explanation:

The student is asking for the equation in point-slope form that represents Byron's distance from home, y, after x hours of running at a constant speed. Considering that Byron's speed is 4 mi/h and after half an hour (0.5 hours) he is 2 miles from home, we can use the information provided to find the point-slope form of the line.

The point-slope form of an equation is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, Byron's running speed represents the slope (4 mi/h), and the point given is (0.5 hours, 2 miles). Substituting these values into the point-slope form gives us y - 2 = 4(x - 0.5).

So, the correct answer is A.