# What is an equation in slope-intercept form of the line that is perpendicular to the graph of #y=2x+3# and passes through (3, -4)?

where:

Find the point-slope form of the perpendicular line.

Plug in the known values.

Simplify.

Simplify.

graph{(y-2x-3)(y+1/2x+5/2)=0 [-11.25, 11.25, -5.625, 5.625]}

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To find the equation of a line perpendicular to ( y = 2x + 3 ), we first determine the slope of the given line, which is ( m = 2 ).

The slope of a line perpendicular to ( y = 2x + 3 ) will have a slope that is the negative reciprocal of ( m ). So, the slope of the perpendicular line is ( -\frac{1}{2} ).

Using 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, and substituting the given point ( (3, -4) ) and the slope ( -\frac{1}{2} ), we get:

( y - (-4) = -\frac{1}{2}(x - 3) )

Simplifying:

( y + 4 = -\frac{1}{2}x + \frac{3}{2} )

( y = -\frac{1}{2}x + \frac{3}{2} - 4 )

( y = -\frac{1}{2}x - \frac{5}{2} )

So, the equation of the line perpendicular to ( y = 2x + 3 ) and passing through ( (3, -4) ) is ( y = -\frac{1}{2}x - \frac{5}{2} ).

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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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