# A line has slope -2 and contains P(3,4) and Q(-4, a). How do you find the value of a?

See full solution process below.

First, we can use the point-slope formula to get the equation for this line since we know the slope and point:

When the problem's slope and point are substituted, the following happens:

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To find the value of ( a ), you can use the point-slope form of the equation of a line:

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

where ( (x_1, y_1) ) is a point on the line and ( m ) is the slope.

Given that the line contains point ( P(3,4) ) and has a slope of ( -2 ), you can plug these values into the point-slope form:

[ y - 4 = -2(x - 3) ]

Now, substitute the x-coordinate of point ( Q ) into the equation and solve for ( y ) to find the value of ( a ):

[ y - 4 = -2(-4 - 3) ] [ y - 4 = -2(-7) ] [ y - 4 = 14 ] [ y = 14 + 4 ] [ y = 18 ]

So, the value of ( a ) is ( 18 ).

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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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