What is the equation of the line with slope # m= 13/7 # that passes through # (7/5,4/7) #?

Answer 1

#65x-35y=71#

The "slope-point form" of the linear equation is #color(white)("XXX")(y-bary)=m(x-barx)# given a slope #m# and a point #(barx,bary)#.
Given that #color(white)("XXX")(barx,bary)=(7/5,4/7)# and #color(white)("XXX")m=13/7#
The "slope-point form" is as follows: #color(white)("XXX")(y-4/7)=13/7(x-7/5)#. This ought to be a legitimate response to the query posed.
But since it looks bad, let's put it in standard form as follows: #color(white)("XXX")Ax+By=C# with #A, B, and C in ZZ, A>=0#
Add #7# to both sides. #color(white)("XXX")7y-4=13x-91/5#
To eliminate the remaining fraction, multiply both sides by #5#: #color(white)("XXX")35y-20=65x-91#
To obtain the variables on one side and the constant on the other, subtract #(35y-91)# from both sides: #color(white)("XXX")71=65x-35y#

Switch sides: 65x-35y=71 #color(white)("XXX")

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Answer 2

To find the equation of the line with a given slope ((m = \frac{13}{7})) that passes through the point ((\frac{7}{5}, \frac{4}{7})), you can use the point-slope form of a linear equation:

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

Where:

  • (m) is the slope of the line.
  • ((x_1, y_1)) are the coordinates of the given point.

In this case:

  • (m = \frac{13}{7})
  • (x_1 = \frac{7}{5})
  • (y_1 = \frac{4}{7})

Plugging these values into the equation:

[y - \frac{4}{7} = \frac{13}{7}(x - \frac{7}{5})]

[y - \frac{4}{7} = \frac{13}{7}x - \frac{13}{5}]

[y = \frac{13}{7}x - \frac{13}{5} + \frac{4}{7}]

[y = \frac{13}{7}x - \frac{13}{5} + \frac{20}{35}]

[y = \frac{13}{7}x - \frac{13}{5} + \frac{20}{35}]

[y = \frac{13}{7}x - \frac{13}{5} + \frac{4}{7}]

[y = \frac{13}{7}x - \frac{65}{35} + \frac{20}{35}]

[y = \frac{13}{7}x - \frac{45}{35}]

[y = \frac{13}{7}x - \frac{9}{7}]

So, the equation of the line with slope (m = \frac{13}{7}) that passes through the point ((\frac{7}{5}, \frac{4}{7})) is (y = \frac{13}{7}x - \frac{9}{7}).

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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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