Question

1. a cyclist travels at a constant rate of 15 miles per hour and starts 5 miles from home.

a. standard form because constants are involved
b. slope - intercept form because the rate and starting value are given
c. point - slope form because time is involved
d. point - slope form because a point is not given

1. the temperature at noon was 72°f and increased steadily by 2°f per hour.

a. point - slope form because a point and slope are given
b. slope - intercept form because the initial value is given
c. standard form because temperature is measured
d. point - slope form because only one value is given

Explanation:

Question 14

To determine the appropriate linear equation form, we analyze the given information: the cyclist's rate (15 miles per hour) is the slope, and the starting distance from home (5 miles) is the y - intercept. Slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Since we have the rate (slope) and the starting value (y - intercept), slope - intercept form is appropriate. Option A is incorrect because standard form is not the best choice here. Option C is incorrect as time being involved doesn't mean point - slope form is needed. Option D is incorrect as a starting point (the 5 - mile mark) is given.

We are given the temperature at noon (a point: when \(x = 0\), \(y=72\)) and the rate of increase (slope \(m = 2\)). Point - slope form is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point and \(m\) is the slope. Option B is incorrect because while the initial value is given, the key here is that we have a point (noon, 72°F) and a slope (2°F per hour), so point - slope is better. Option C is incorrect as standard form is not related to temperature measurement. Option D is incorrect as we have two values: a point and a slope.

Answer:

B. Slope - intercept form because the rate and starting value are given

Question 15