Question

Byron's workout starts with a warmup 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 = 2x - 4
d) y = 2x

Answer 1

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

Step-by-step explanation:

The student has asked for an equation in point-slope form that represents Byron's distance from home, y, after x hours of running at a speed of 4 mi/h. Given that after half an hour (0.5 hours), Byron is 2 miles from home, we can use this information to derive the equation.

The point-slope form of a line's equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Here, the slope (m) is Byron's running speed, which is 4 miles per hour, and the point we can use is (0.5, 2) since after 0.5 hours, the distance from home is 2 miles.

Substituting these values into the point-slope form yields the equation:

y - 2 = 4(x - 0.5)

Therefore, the correct answer is a) y - 2 = 4(x - 0.5).