Question

Nhich equation represents a line that passes through (2, -1/2) and has a slope of 3?

A) y-2 = 3(x +
B) y-3 = 2(x + 1)
C) y+ 1 = 3(x - 2)
D) y+ 1 = 2x – 3)

Answer 1

The correct linear equation that passes through the point (2, -1/2) with a slope of 3 is represented by the equation y + 1 = 3(x - 2), which matches option C when simplified.

Step-by-step explanation:

The equation that represents a line passing through the point (2, -1/2) with a slope of 3 is given by the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Given that the slope (m) is 3, we can start with the equation y = 3x + b. To find b, we plug in the given point (2, -1/2) into the equation. This results in -1/2 = 3(2) + b. Solving for b gives us b = -1/2 - 6 = -6.5. Thus, the correct equation is y = 3x - 6.5. Among the options provided, the one that matches this form when simplified is option C: y + 1 = 3(x - 2).