In the equation Y - 5 = -2(X + 3), what does the coefficient -2 represent?

In the equation Y - 5 = -2(X + 3), what does the coefficient -2 represent?

• A. The slope
• B. The y-intercept
• C. The x-intercept
• D. The constant term

Answer: (A)

In the equation Y - 5 = -2(X + 3), the coefficient -2 corresponds to the slope of the line when the equation is rearranged into slope-intercept form (Y = mx + b), where "m" represents the slope and "b" represents the y-intercept. To analyze this, we can transform the given equation into slope-intercept form. Starting with Y - 5 = -2(X + 3), we first distribute -2: Y - 5 = -2X - 6. Next, we add 5 to both sides: Y = -2X - 1. From this rearrangement, we see that the coefficient of X, which is -2, directly indicates the slope of the line. The slope provides us with information about the steepness and direction of the line: a negative slope means that as the value of X increases, the value of Y decreases. This distinction is crucial. The other options do not accurately reflect what the coefficient -2 represents. The y-intercept refers to where the line crosses the Y-axis, the x-intercept is where it crosses the X-axis, and the constant term refers to specific additive values independent of the slope or intercepts

In the equation Y - 5 = -2(X + 3), the coefficient -2 corresponds to the slope of the line when the equation is rearranged into slope-intercept form (Y = mx + b), where "m" represents the slope and "b" represents the y-intercept.

To analyze this, we can transform the given equation into slope-intercept form. Starting with Y - 5 = -2(X + 3), we first distribute -2:

Y - 5 = -2X - 6.

Next, we add 5 to both sides:

Y = -2X - 1.

From this rearrangement, we see that the coefficient of X, which is -2, directly indicates the slope of the line. The slope provides us with information about the steepness and direction of the line: a negative slope means that as the value of X increases, the value of Y decreases.

This distinction is crucial. The other options do not accurately reflect what the coefficient -2 represents. The y-intercept refers to where the line crosses the Y-axis, the x-intercept is where it crosses the X-axis, and the constant term refers to specific additive values independent of the slope or intercepts