Answer:
C. [tex]y + \frac{1}{2} = 3(x - 2)[/tex]
Step-by-step explanation:
Given
[tex]Point: (2,\frac{-1}{2})[/tex]
[tex]Slope: 3[/tex]
Required
Equation of line
Let m represents the slope of the line;
m is calculated as thus
[tex]m = \frac{y - y_1}{x - x_1}[/tex]
[tex]where (x_1,y_1) = (2,\frac{-1}{2})[/tex]
[tex]So; x_1 = 2; y_1 = \frac{-1}{2}[/tex]
[tex]m = 3[/tex]
By substituting the right values in the formula above;
[tex]m = \frac{y - y_1}{x - x_1}[/tex] becomes
[tex]3 = \frac{y - \frac{-1}{2}}{x - 2}[/tex]
Multiply both sides by [tex](x - 2)[/tex]
[tex]3 *(x - 2) = \frac{y - \frac{-1}{2}}{x - 2} *(x - 2)[/tex]
[tex]3 *(x - 2) = (y - \frac{-1}{2})[/tex]
[tex]3 *(x - 2) = (y + \frac{1}{2})[/tex]
[tex]3(x - 2) = (y + \frac{1}{2})[/tex]
[tex]3(x - 2) = y + \frac{1}{2}[/tex]
Reorder
[tex]y + \frac{1}{2} = 3(x - 2)[/tex]
Hence, the equation that represents the line is [tex]y + \frac{1}{2} = 3(x - 2)[/tex]
