1. The slope intercept form is:
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is the slope of the line and [tex]b[/tex] is the intercept with the y-axis.
2. To calculate the slope, you can use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where:
[tex]y_2=-1\\y_1=\frac{15}{2}\\x_2=\frac{1}{8}\\x_1=-2[/tex]
3. So:
[tex]m=\frac{-1-(\frac{15}{2})}{\frac{1}{8}-(-2)}=-4[/tex]
4. Now you must find [tex]b[/tex]. Substitute any of the given points into the equation and solve for [tex]b[/tex]:
[tex]\frac{15}{2}=-4(-2)+b\\\frac{15}{2}=8+b\\b=-\frac{1}{2}[/tex]
5. Therefore, the answer is the last option:
[tex]y=-4x-\frac{1}{2}[/tex]
