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Find the equation of a line containing the given points. Write the equation in slope-intercept form (-2, -5) and (-5, -8)

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Answer


y=x-3

Step-by-step explanation

The equation in slope-intercept form is:


y=mx+b

where m is the slope and b is the y-intercept.

Additionally, the slope m can be calculated using the change between two points as it is a line and will be the same in all points:


m=(y_2-y_1)/(x_2-x_1)

Considering the two points given, we can assume that point one is (-2, -5) and point two is (-5, -8). Replacing these values we get:


m=(-8-(-5))/(-5-(-2))

Simplifying:


m=(-8+5)/(-5+2)=(-3)/(-3)=1

Then, replacing the slope calculated in the equation we get:


y=(1)x+b

Next, we have to choose one of the given points to replace in the equation and solve for b. For example, choosing (-2,-5):


-5=(1)(-2)+b
-5=-2+b
b=-5+2
b=-3

Finally, our equation is:


y=x-3

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