Final answer:
The correct equation is y = -3/2x + 6 (Option B). The equation is linear in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Step-by-step explanation:
The correct equation is y = -3/2x + 6 (Option B). This equation is linear because it is in the form y = mx + b, where m represents the slope and b represents the y-intercept.
In the given equation, the slope is -3/2, which means that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 3/2. The y-intercept is 6, which is the value of y when x = 0.
The question asks which of the given equations is the correct representation of a specific linear equation. According to the provided information, the equation for the line is 'y = 9 + 3x'. This means we are looking for an equation with a positive slope (m) of 3 and a y-intercept (b) of 9. The general form of a linear equation is y = mx + b, where 'm' is the slope, and 'b' is the y-intercept. Evaluating the options:
A. y = -2/3x + 6 has a slope of -2/3 and y-intercept of 6.
B. y = -3/2x + 6 has a slope of -3/2 and y-intercept of 6.
C. y = 2/3x + 9 has a slope of 2/3 and y-intercept of 9.
D. y = 3/2x + 9 has a slope of 3/2 and y-intercept of 9.