# What is the equation of a line that goes through #(-6, 3)# and has a slope of #-2/3#?

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Plug in the numbers

Solve

So

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The equation of the line can be expressed in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. Given that the slope (m) is -2/3 and a point on the line is (-6, 3), we can substitute these values into the equation and solve for the y-intercept (b).

Using the point-slope form: y - y₁ = m(x - x₁), where (x₁, y₁) = (-6, 3), and m = -2/3:

y - 3 = (-2/3)(x - (-6)) y - 3 = (-2/3)(x + 6) y - 3 = (-2/3)x - 4 y = (-2/3)x - 4 + 3 y = (-2/3)x - 1

Therefore, the equation of the line is y = (-2/3)x - 1.

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The equation of the line passing through the point (-6, 3) with a slope of -2/3 is:

[ y - y_1 = m(x - x_1) ]

Where ( (x_1, y_1) ) is the given point and ( m ) is the slope.

Substituting the given values:

[ y - 3 = -\frac{2}{3}(x + 6) ]

Now, simplify the equation:

[ y - 3 = -\frac{2}{3}x - 4 ]

[ y = -\frac{2}{3}x - 1 ]

So, the equation of the line is ( y = -\frac{2}{3}x - 1 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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