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4 years ago

Graphing in Point-Slope Form y−y1=m(x−x1) Graph the equation y+7=−45(x−4) ?

Mathematics

1 answer:

nevsk [136]4 years ago

3 0

Answer:

<h2>The graph is in the attachment.</h2>

Step-by-step explanation:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

m - slope

(x₁, y₁) - a point on a line

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

We have the equation in a point-slope form:

$y+7=-\dfrac{4}{5}(x-4)$

$y-(-7)=-\dfrac{4}{5}(x-4)$

Therefore we have one point: (4, -7).

Convert to the slope-intercept form:

$y+7=-\dfrac{4}{5}(x-4)$ use the distributive property

$y+7=-\dfrac{4}{5}x+\left(-\dfrac{4}{5}\right)(-4)$

$y+7=-\dfrac{4}{5}x+\dfrac{16}{5}$

$y+7=-\dfrac{4}{5}x+3\dfrac{1}{5}$ subtract 7 from both sides

$y=-\dfrac{4}{5}x-3\dfrac{4}{5}$

Put x = -1 to the equation:

$y=-\dfrac{4}{5}(-1)-3\dfrac{4}{5}=\dfrac{4}{5}-3\dfrac{4}{5}=-3$

Therefore we have the second point (-1, -3).

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Solve question 13. And 14. Please!! Will reward brainliest!!

SIZIF [17.4K]

Answer:

y = 4 sin( 0.5t - $\frac{4\pi }{3}$ ) - 2

y = a sin ( 2t - $\frac{-\pi }{3}$ ) + 2

Step-by-step explanation:

In the first question,

amplitude = 4

Period = $4\pi$

phase shift = $\frac{-4\pi }{3}$

Vertical shift = -2

Angular velocity , w = $\frac{2\pi }{time period}$

Here, w = $\frac{2\pi }{4\pi }$ = 0.5

The general equation of a wave is

y = a sin( wt + ∅ )

Putting above values in the equation,

y = 4 sin( 0.5t - $\frac{4\pi }{3}$ ) - 2

In the second question,

Amplitude is not given so we will take it as a.

time period = $\pi$

w = 2

Phase shift = $\frac{-\pi }{3}$

Vertical shift = 2

The equation is

y = a sin ( 2t - $\frac{-\pi }{3}$ ) + 2

5 0

3 years ago

Need help with homework

motikmotik

We have two points describing the diameter of a circumference, these are:

$\begin{gathered} A=(-12,-4) \\ B=(-4,-10) \end{gathered}$

Recall that the equation for the standard form of a circle is:

$(x-h)^2+(y-k)^2=r^2$

Where (h,k) is the coordinate of the center of the circle, to find this coordinate, we find the midpoint of the diameter, that is, the midpoint between points A and B.

For this we use the following equation:

$M=(\frac{x_1+x_2_{}_{}}{2},\frac{y_1+y_2}{2})$

Now, we replace and solve:

$\begin{gathered} M=(\frac{-12+(-4)}{2},\frac{-4+(-10)}{2} \\ M=(\frac{-12-4}{2},\frac{-4-10}{2}) \\ M=(\frac{-16}{2},\frac{-14}{2}) \\ M=(-8,-7) \end{gathered}$

The center of the circle is (-8,-7), so:

$\begin{gathered} h=-8 \\ k=-7 \end{gathered}$

On the other hand, we must find the radius of the circle, remember that the radius of a circle goes from the center of the circumference to a point on its arc, for this we use the following equation: