Question

Which of the following equations represent a linear function that passes through the point (5,-2) with a slope of -3?

y-y₁ = m(x-x1
Ay-2=3(x - 5)
By+2=-3 (x - 5)
Cy+2=3(x - 5)
Dy-2=-3 (x - 5)

Answer 1

Option B, y+2 = -3(x - 5), is the correct equation that represents a linear function with a slope of -3, passing through the point (5, -2).

Step-by-step explanation:

The student is asking which equation represents a linear function that passes through a given point with a particular slope. A linear function can be written in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Given the point (5, -2) and a slope of -3, we plug these into the equation to find the equation of the line.

The correct equation of the line is: y - (-2) = -3(x - 5), which simplifies to y + 2 = -3(x - 5). Therefore, option B is the correct answer. Now let's check the given options:

• Option A: y-2 = 3(x - 5). This equation has a positive slope of 3, which is not the required slope of -3.
• Option B: y+2 = -3 (x - 5). This equation correctly represents a slope of -3 through the point (5, -2).
• Option C: y+2 = 3(x - 5). This equation also has a positive slope of 3, incorrect for our requirement.
• Option D: y-2 = -3 (x - 5). This equation would be correct if the given point was (5, 2) instead of (5, -2).