Question

Which equation represents a line that passes through (2, –left-parenthesis 2, negative StartFraction one-half EndFraction right-parenthesis.) and has a slope of 3?

y – 2 = 3(x + y minus 3 equals 2 left-parenthesis x plus StartFraction one-half EndFraction right-parenthesis.)
y – 3 = 2(x + y minus 3 equals 2 left-parenthesis x plus StartFraction one-half EndFraction right-parenthesis.)
y + y plus StartFraction one-half EndFraction equals 3 left-parenthesis x minus 2 right-parenthesis. = 3(x – 2)
y + y plus StartFraction one-half EndFraction equals 2 left-parenthesis x minus 3 right-parenthesis. = 2(x – 3)

Answer 1

Point-slope form: y - y1 = m(x - x1). With (2, -1/2) and m = 3:

y - (-1/2) = 3(x - 2) → y + 1/2 = 3(x - 2).

(Equivalently y = 3x - 13/2.) So choose the option y + 1/2 = 3(x − 2).