How do you write the equation of a line in slope intercept, point slope and standard form given Point: (5,-8) and is parallel to y=9x+4?

Answer 1

Slope intercept form of the equation is #y=9x-53#, point slope form is #y+8=9(x-5)#, and standard form is #-9x+y=-53#

Lines that are parallel have the same slope. Knowing this, the slope is #9#, so #m=9# in each of the forms
Slope intercept form: #y=mx+b#

First plug in the slope:

#y=9x+b#
Next we have to solve for #b# which is done by plugging in the point that was given #(5,-8)# for #x# and #y#:
#-8=9(5)+b#
#-8=45+b#
#b=-53#
Now that we know b, we can plug it in to the slope intercept form, giving us #y=9x-53#
Point slope form: #y-y_1=m(x-x_1)#
Plug in the slope, which is #9#
#y-y_1=9(x-x_1)#
Plug the point that is given, #(5,-8)#, into the point slope form:
#y-(-8)=m(x-(5))#

Simplify, giving you the final answer for point slope form:

#y+8=9(x-5)#
Finally, standard form which is #ax+by=c#

To get standard form we can use slope intercept form which we know is

#y=9x-53#
Subtract #9x# from both sides, giving you standard form:
#-9x+y=-53#
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Answer 2

Slope-intercept form: y = 9x - 53 Point-slope form: y + 8 = 9(x - 5) Standard form: 9x - y = 53

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Answer 3

Slope-intercept form: [ y = mx + b ] [ m = 9 ] (since the given line ( y = 9x + 4 ) is parallel) [ x_1 = 5, \space y_1 = -8 ] (given point) [ -8 = 9(5) + b ] [ b = -53 ] [ \boxed{y = 9x - 53} ]

Point-slope form: [ y - y_1 = m(x - x_1) ] [ m = 9 ] (since the given line ( y = 9x + 4 ) is parallel) [ x_1 = 5, \space y_1 = -8 ] (given point) [ y - (-8) = 9(x - 5) ] [ y + 8 = 9x - 45 ] [ \boxed{y = 9x - 53} ]

Standard form: [ Ax + By = C ] [ m = 9 ] (since the given line ( y = 9x + 4 ) is parallel) [ x_1 = 5, \space y_1 = -8 ] (given point) [ -8 = 9(5) + b ] [ -8 = 45 + b ] [ b = -53 ] [ y = 9x - 53 ] [ 9x - y = 53 ] [ \boxed{9x - y = 53} ]

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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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