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

Answer

$y=x-3$

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:

$m=\frac{y_2-y_1}{x_2-x_1}$

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:

$m=\frac{-8-(-5)}{-5-(-2)}$

Simplifying:

$m=\frac{-8+5}{-5+2}=\frac{-3}{-3}=1$

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:

$y=x-3$