What is the equation of the line between #(10,3)# and #(-4,12)#?

Answer 1

#y=-9/14 x + 9 3/7#

Working on the assumption that you are talking about a straight line graph

Standard equation form is: #y=mx+c#
#x# is the independent variable
#y# is the dependant variable (its value 'depends' on what you assign to #x#
#m# is the gradient of the line (slope) #color(white)(XXX)#going from left to right, a positive #color(white)(XXX)#slop is upwards and a negative slope is downwards.
#c# is a constant value and is where the line intersects the y-axis.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("To find the gradient:")# The amount of up (or down) for the amount of along. That is:
#m=("change in the y-axis")/("change in the x-axis")#
Let #(x_1 ,y_1)-> (10,3)# Let #x_2,y_2)->(-4,12)#
so #m= (y_2-y_1)/(x_2-x_1) -> (12-3)/((-4)-10) = 9/(-14)#
#color(blue)(m=-9/14)# which is negative so the line descends from left to right ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("To find the constant")#
We can substitute known value for #x# and #y# to find #c# I am choosing #color(brown)((x_1 ,y_1)-> (10,3))#
So #y_1=mx_1+c# becomes:
#color(brown)(3=color(blue)(-9/14)(10)+color(black)(c))#
#c=3+(9xx10)/14#
#color(blue)(c=3+6 3/7= 9 3/7)# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Putting it all together:
#y=-9/14 x + 9 3/7#
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Answer 2

The equation of the line passing through the points (10, 3) and (-4, 12) can be found using the point-slope form of a linear equation. The formula is ( y - y_1 = m(x - x_1) ), where ( (x_1, y_1) ) is a point on the line and ( m ) is the slope of the line.

First, find the slope ( m ) using the formula ( m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ), where ( (x_1, y_1) = (10, 3) ) and ( (x_2, y_2) = (-4, 12) ).

( m = \frac{{12 - 3}}{{-4 - 10}} = \frac{{9}}{{-14}} )

Now that we have the slope, we can use one of the given points and the slope in the point-slope form to find the equation of the line. Let's use the point ( (10, 3) ).

( y - 3 = \frac{{9}}{{-14}}(x - 10) )

Simplify:

( y - 3 = -\frac{{9}}{{14}}x + \frac{{90}}{{14}} )

( y = -\frac{{9}}{{14}}x + \frac{{90}}{{14}} + 3 )

( y = -\frac{{9}}{{14}}x + \frac{{90 + 42}}{{14}} )

( y = -\frac{{9}}{{14}}x + \frac{{132}}{{14}} )

( y = -\frac{{9}}{{14}}x + 9 )

So, the equation of the line passing through the points (10, 3) and (-4, 12) is ( y = -\frac{{9}}{{14}}x + 9 ).

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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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