Question

find the x and y intercepts of the line that passes through the given points (-5,-5), (10,-2)x intercept =y intercept =

Answer 1

The equation of line passing through the points is given by,

`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

Let,

`\begin{gathered} (x_(1,)y_1)=(-5,\text{ -5}) \\ (x_(2,)y_2)=(10,\text{ -2)} \end{gathered}`

Then the equation of the line is,

`\begin{gathered} (y-(-5))/(-2-(-5))=(x-(-5))/(10-(-5)) \\ (y+5)/(3)=(x+5)/(15) \\ 15y+75=3x+15 \\ 3x-15y=60 \\ x-5y=20 \\ \end{gathered}`

Converting the above equation into the intercept form,

Dividing the equation on both sides by 20,

`\begin{gathered} (x)/(20)-(5y)/(20)=1 \\ (x)/(20)+(y)/(-4)=1 \end{gathered}`

On comparing the above equation with the intercept form

`(x)/(a)+(y)/(b)=1`

We get,

x-intercept is, a=20 and the y-intercept is, b=-4