Answer:
y = (-7/3)x - 26/3
Step-by-step explanation:
To find the equation of a line given two points, we can first define an equation of a line to be y= mx +b, with m being the slope and b being the y intercept.
To calculate the slope, we can use the formula (change in y)/(change in x), or
(y₂-y₁)/(x₂-x₁). If we define (-2, -4) as point 1 (meaning -2 is x₁ and -4 is y₁) and (-8, 10) as point 2 (it doesn't matter which point is point 1/2), we can say that the slope is equal to
(10-(-4)) / (-8-(-2)
= 14/(-6)
= -7/3
Therefore, our formula so far is
y = (-7/3)x + b
To figure out b, we can plug in a point, e.g. (-8, 10) and solve for b. Plugging this in, we get
10 = (-7/3)(-8) + b
10 = 56/3 + b
subtract 56/3 from both sides
10 - 56/3 = b
= 30/3 - 56/3
= -26/3
Therefore, our equation is
y = (-7/3)x - 26/3
