Find the equation of the line in slope-intercept form containing the points (6, -1) and (-3, 2).

Solution:

It is given that pair of points. (6, -1), (-3, 2).

The slope of the Line that Passes Through (x₁, y₁) and (x₂, y₂) is given by:

Slope (m) = (y₂ - y₁) / (x₂ - x₁)

So, (x₁, y₁) = (6, -1) and (x₂, y₂) = (-3, 2)

Now, Substitute (x₁, y₁) and (x₂, y₂) with their given values, we get,

m = (- 1 - 2)/(6 - (-3))

m = (-3) / (9)

m = -1/3

Now use the slope and point (2, 3) to find the y-intercept.

y = mx + b

⇒ -1 = (-1/3)(6) + b

⇒ -1 = -6/3 + b

⇒ -1 = -2 + b

⇒ b = 2 - 1

⇒ b = 1

So, y = -1/3x + 1

Therefore, the equation of the line is y= -1/3x + 1.

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Find the equation of the line in slope-intercept form containing the points (6, -1) and (-3, 2).

Summary:

The equation of the line in slope-intercept form containing the points (6, -1) and (-3, 2) is y = -1/3x + 1.