Question

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

Answer 1

`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`