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3 years ago

Identify an equation in slope intercept form for the line parallel to Y equals 4X -9 that passes through (-5,3)

Mathematics

1 answer:

Kobotan [32]3 years ago

7 0

Slope intercept form of a line is y=mx+b where m= slope and b=y-intercept.

Now compare this form with the tiven equation y=4x-9 to get the value of m.

So, m= 4.

Slope of all parallel lines are always equal. Which means the line which is parallel to this has also the same slope: m=4.

Now we need to find the value of b to get the equation. That parallel line passes through (-5,3).

The point intercept form of a line is,

(y-y1)=m(x-x1)

So, we can plug in the m=4, x1=-5 and y1=3 in the above equation. Hence,

y-3=4(x-(-5))

y-3=4(x+5) Since -(-5)=+5

y-3=4x+20 By distributing property.

y=4x+20+3 Adding 3 to each sides.

y=4x+23

So, the slope-intercept form of that parallel line is y=4x+23.

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Read 2 more answers

Graph the hyperbola using the transverse axis, vertices, and co-vertices:

Reptile [31]

See attachment for the graph of the hyperbola 12x^2 - 3y^2 - 108 = 0

<h3>How to graph the hyperbola?</h3>

The equation of the hyperbola is given as:

12x^2 - 3y^2 - 108 = 0

Start by calculating the transverse axis

So, we have:

<u>Transverse axis</u>

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

Where

a = 3 and b = 6

The transverse axis is calculated as:

y = ±b/a(x - h) + k

So, we have:

y = ±6/3(x - 0) + 0

Evaluate the difference and sum

y = ±6/3x

Evaluate the quotient

y = ±2x

This means that the transverse axes are y = 2x and y =-2x

<u>The vertices</u>

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

<u>The co-vertices</u>

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

And

a = 3 and b = 6

The co-vertices are

(h - a, k) and (h + a, k)

So, we have:

(0 - 3, 0) and (0 + 3, 0)

Evaluate

(-3,0) and (3, 0)

See attachment for the graph of the hyperbola