Question

section 4: linear equation forms (questions 13–15)
choose the best form of a linear equation to model the situation.

1. a plant is 12 cm tall and grows 3 cm per week.

a. point - slope form because a point is given
b. standard form because two variables are related
c. slope - intercept form because the slope and initial value are given
d. point - slope form because the slope is given

Explanation:

To determine the best linear equation form, analyze the given situation: the plant's initial height (12 cm, which is the y - intercept) and the growth rate (3 cm per week, which is the slope) are provided. The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept (initial value). Option A is incorrect because point - slope form is better when a point and slope are given, but here we have an initial value (y - intercept) and slope. Option B is incorrect as standard form ($Ax+By = C$) is not the best fit here since we have a slope and initial value. Option D is incorrect as point - slope form is not the right choice here as we have the initial value (y - intercept) and slope, not just a point and slope. Option C is correct because slope - intercept form is suitable when the slope ($m = 3$) and initial value ($b = 12$) are given.

Answer:

C. Slope - intercept form because the slope and initial value are given