Answer:
[tex]y = - \frac{5}{4} x - \frac{1}{2} [/tex]
Step-by-step explanation:
Slope-intercept form: y= mx +c, where m is the slope and c is the y-intercept.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope
[tex] = \frac{ - 3 - \frac{1}{8} }{2 - ( - \frac{1}{2}) } [/tex]
[tex] = - \frac{5}{4} [/tex]
Substitute the value of m into the equation:
[tex]y = - \frac{5}{4} x + c[/tex]
To find the value of c, substitute a pair of coordinates the line passes through into the equation.
When x= 2, y= -3,
[tex] - 3 = - \frac{5}{4} (2) + c[/tex]
[tex] - 3 = - \frac{5}{2} + c[/tex]
[tex]c = - 3 + \frac{5}{2} [/tex]
[tex]c = - \frac{1}{2} [/tex]
Thus, the equation of the line is [tex]y = - \frac{5}{4} x - \frac{1}{2} [/tex].
