Question

Find the X and y intercepts of the line that passes through the given points(-6,-6),(6,-3)

Answer 1

We will find the x & y-intercepts as follows:

*First: We will calculate the slope:

`m=(-3-(-6))/(6-(-6))\Rightarrow m=(1)/(4)`

*Second: We will replace this slope and one of the points in the following expression:

`y-y_1=m(x-x_1)`

That is:

`y-(-3)=((1)/(4))(x-6)\Rightarrow y+3=(1)/(4)x-(3)/(2)`
`\Rightarrow y=(1)/(4)x-(9)/(2)`

*Third: We will find the x & y-components:

*x-component: We replace y = 0 and solve for x:

`0=(1)/(4)x-(9)/(2)\Rightarrow(1)/(4)x=(9)/(2)\Rightarrow x=18`

So, the x-intercept is located at (18, 0).

*y-intercept: We replace x = 0 and solve for y:

`y=(1)/(4)(0)-(9)/(2)\Rightarrow y=-(9)/(2)`

So, the y-intercept is located at (0, -9/2).