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

For this case we have that by definition, the equation of a line in the point-slope form is given by:

$y-y_ {0} = m (x-x_ {0})$

Where:

m: It is the slope of the line

$(x_ {0}, y_ {0}):$ It is a point through which the line passes

According to the data of the statement we have to:

$(x_ {0}, y_ {0}) :( 2, - \frac {1} {2})\\m = 3$

We replace:

$y - (- \frac {1} {2}) = 3 (x-2)\\y + \frac {1} {2} = 3 (x-2)$

Answer:

$y + \frac {1} {2} = 3 (x-2)$