Which equation is the equation of a line that passes through (-10. 3) and is perpendicular to #y=5x-7#?

Answer 1

#y=-1/5 x +1#

I assume there is a typo and the problem should be:

write the equation of a line that passes through #(-10,3)# and is perpendicular to #y=5x-7#.
The line #y=5x-7# is in slope-intercept form #y=mx+b# where #m# is the slope. The slope of this line is thus #m=5#.

Perpendicular lines have slopes which are negative reciprocals. In other words, take the reciprocal of the slope and change the sign.

The negative reciprocal of #5# is #-1/5#.
To find the equation of a line which passes through #(color(red)(-10),color(red)3)# and with a slope of #color(blue)m= color(blue)(-1/5)#, use the point- slope formula:
#y-color(red)(y_1)=color(blue)m(x-color(red)(x_1))# where #(color(red)(x_1),color(red)( y_1))# is a point and #color(blue)m# is the slope.
#y-color(red)(3)=color(blue)(-1/5)(x-color(red)(-10))#
#y-3=-1/5(x+10)color(white)(aaa)# Equation in point-slope form
To put the equation in slope-intercept form, distribute the #-1/5#.
#y-3=-1/5 x-2#

Add 3 to both sides.

#y-3=-1/5 x-2# #color(white)a+3color(white)(aaaaaaaa)+3#
#y=-1/5 x +1#
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Answer 2

The equation of the line that passes through (-10, 3) and is perpendicular to (y = 5x - 7) is (y = -\frac{1}{5}x + 1).

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Answer from HIX Tutor

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.

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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