Sagot :
The equation of line passing through the points is given by,
[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}[/tex]Let,
[tex]\begin{gathered} (x_{1,}y_1)=(-5,\text{ -5}) \\ (x_{2,}y_2)=(10,\text{ -2)} \end{gathered}[/tex]Then the equation of the line is,
[tex]\begin{gathered} \frac{y-(-5)}{-2-(-5)}=\frac{x-(-5)}{10-(-5)} \\ \frac{y+5}{3}=\frac{x+5}{15} \\ 15y+75=3x+15 \\ 3x-15y=60 \\ x-5y=20 \\ \end{gathered}[/tex]Converting the above equation into the intercept form,
Dividing the equation on both sides by 20,
[tex]\begin{gathered} \frac{x}{20}-\frac{5y}{20}=1 \\ \frac{x}{20}+\frac{y}{-4}=1 \end{gathered}[/tex]On comparing the above equation with the intercept form
[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]We get,
x-intercept is, a=20 and the y-intercept is, b=-4