# How do you write an equation for a line passing through the points (5,-1) and (-3,-2)?

The equation of the line in standard form is

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To write an equation for a line passing through the points (5, -1) and (-3, -2), you can use the point-slope form of a linear equation: ( y - y_1 = m(x - x_1) ), where ( m ) is the slope and ( (x_1, y_1) ) is one of the given points.

- First, calculate the slope (( m )) using the formula ( m = \frac{y_2 - y_1}{x_2 - x_1} ), where ( (x_1, y_1) ) and ( (x_2, y_2) ) are the given points.
- Then, choose one of the given points and substitute its coordinates into the point-slope form along with the calculated slope to get the equation of the line.

Using the given points:

( (x_1, y_1) = (5, -1) ) and ( (x_2, y_2) = (-3, -2) )

- Calculate the slope (( m )):

( m = \frac{-2 - (-1)}{-3 - 5} = \frac{-2 + 1}{-3 - 5} = \frac{-1}{-8} = \frac{1}{8} )

- Choose one of the points, let's say (5, -1), and substitute into the point-slope form:

( y - (-1) = \frac{1}{8}(x - 5) )

Simplify:

( y + 1 = \frac{1}{8}(x - 5) )

Distribute:

( y + 1 = \frac{1}{8}x - \frac{5}{8} )

Subtract 1 from both sides:

( y = \frac{1}{8}x - \frac{5}{8} - 1 )

Simplify:

( y = \frac{1}{8}x - \frac{5}{8} - \frac{8}{8} )

( y = \frac{1}{8}x - \frac{13}{8} )

So, the equation of the line passing through the points (5, -1) and (-3, -2) is ( y = \frac{1}{8}x - \frac{13}{8} ).

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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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