How do you find a equation of the line containing the given pair of points (-5,0) and (0,9)?

Answer 1

I found: #9x-5y=-45#

I would try using the following relationship:

#color(red)((x-x_2)/(x_2-x_1)=(y-y_2)/(y_2-y_1))#
Where you use the coordinate of your points as: #(x-0)/(0-(-5))=(y-9)/(9-0)# rearranging: #9x=5y-45# Giving: #9x-5y=-45#
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Answer 2

#y=(9/5)*x+9#

You are searching the equation of a straight line (=linear equation) who contain #A(-5,0) and B(0,9)#
A linear equation form is : #y=a*x+b#, and here we will try to find numbers #a# and #b#
Find #a# :
The number #a# representing the slope of the line.
#a = (y_b-y_a)/(x_b-x_a) = Delta_y/Delta_x#
with #x_a# representing the abscissa of the point #A# and #y_a# is the ordinate of the point #A#.
Here, #a = (9-0)/(0-(-5)) = 9/5#
Now our equation is : #y=(9/5)*x+b#
Find #b# :
Take one point given, and replace #x# and #y# by the coordinate of this point and find #b#.
We are lucky to have one point with #0# in abscissa, it makes the resolution easier :
#y_b = (9/5)*x_b + b# # 9 = (9/5)*0 + b# # b = 9 #

Therefore, we have the equation line !

#y = (9/5)*x+9#
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Answer 3

To find the equation of the line containing the given pair of points (-5,0) and (0,9), you can use the point-slope form of a linear equation.

  1. Calculate the slope using the formula: ( m = \frac{y_2 - y_1}{x_2 - x_1} ).
  2. Choose one of the points and plug the slope into the point-slope form equation: ( y - y_1 = m(x - x_1) ).

Let's calculate the slope:

( m = \frac{9 - 0}{0 - (-5)} = \frac{9}{5} ).

Now, we'll choose one of the points, let's say (-5,0), and plug the values into the point-slope form equation:

( y - 0 = \frac{9}{5}(x - (-5)) ).

Simplify:

( y = \frac{9}{5}(x + 5) ).

This is the equation of the line in slope-intercept form. We can distribute to put it in standard form if needed.

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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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