Write an equation of the line that passes through the points (-8, -1) and (-5, 9).
To write an equation of the line that passes through the given points, we can use the point-slope form of a linear equation. The point-slope form is given by:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is a point on the line and m is the slope of the line.
Let's calculate the slope (m):
m = (y₂ - y₁) / (x₂ - x₁)
Given point 1: (-8, -1)
Given point 2: (-5, 9)
Substituting the values into the formula, we get:
m = (9 - (-1)) / (-5 - (-8))
= 10 / 3
Now, we have the slope (m = 10/3) and one of the points (x₁, y₁) = (-8, -1).
Plugging these values into the point-slope form equation, we get:
y - (-1) = (10/3)(x - (-8))
Simplifying further:
y + 1 = (10/3)(x + 8)
Now, we can convert the equation to slope-intercept form (y = mx + b), where b is the y-intercept.
y + 1 = (10/3)(x + 8)
Distributing the (10/3):
y + 1 = (10/3)x + (10/3)(8)
= (10/3)x + 80/3
Subtracting 1 from both sides:
y = (10/3)x + 80/3 - 3/3
= (10/3)x + 77/3
So, the equation of the line that passes through the points (-8, -1) and (-5, 9) is:
y = (10/3)x + 77/3