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

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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).

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