Write an equation in point-slope form of the line that passes through the given points, then write the equation in slope-intercept forr
(-6,6), (6,2)
What is the point-slope form of the equation of the line?
To find the equation in point-slope form, we first need to find the slope of the line. The slope can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the given points (-6, 6) and (6, 2) into the formula, we have:
m = (2 - 6) / (6 - (-6))
m = -4 / 12
m = -1/3
Now that we have the slope, we can use the point-slope form of the equation:
y - y₁ = m(x - x₁)
Substituting the values of (x₁, y₁) = (-6, 6) and m = -1/3 into the equation, we have:
y - 6 = (-1/3)(x - (-6))
y - 6 = (-1/3)(x + 6)
This is the equation in point-slope form.
To convert it to slope-intercept form (y = mx + b), we need to simplify the equation:
y - 6 = (-1/3)x - 2
y = (-1/3)x - 2 + 6
y = (-1/3)x + 4
Therefore, the equation in slope-intercept form is y = (-1/3)x + 4.