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3 years ago

Y = 4x + 3

2 answers:

3 0

D) perpendicular!
A perpendicular's definition is: a straight line at an angle of 90° to a given line, plane, or surface.
And if you mark them on a graph you could see these two are opposite of each other.

Likurg_2 [28]3 years ago

3 0

Answer:

Perpendicular.

D is the correct option.

Step-by-step explanation:

The given equations are

$y=4x+4\\\\y=-\frac{1}{4}x-4$

The slope intercept form of a line is given by

$y=mx+b$

Here, m is the slope and b is the y intercept.

Comparing given equation with slope intercept form of the line

Slope of first line = 4

Slope of second line = -1/4

These two slopes are not equal hence, lines are not parallel.

We can see that -1/4 is the negative reciprocal of 4. Since.

$4\cdot-\frac{1}{4}=-1$

We know that the slopes of perpendicular lines are negative reciprocal of each other.

Hence, the lines are perpendicular.

D is the correct option.

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Elina [12.6K]

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3 years ago

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Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directric of x = -2?

vagabundo [1.1K]

Check the picture below. So,the parabola looks like so, notice the distance "p". since the parabola is opening to the right, then "p" is positive, thus is 5.

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
\boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\
(x-{{ h}})^2=4{{ p}}(y-{{ k}}) \\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\$

$\bf -------------------------------\\\\
\begin{cases}
h=3\\
k=1\\
p=5
\end{cases}\implies (y-1)^2=4(5)(x-3)\implies (y-1)^2=20(x-3)
\\\\\\
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3 years ago

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chubhunter [2.5K]

Answer:

Ok, we know that we can write a horizontal translation as:

y' = f(x - A)

where if A is positive, this moves the graph of f(x) A units to the right.

Why is this?

Ok, let's compare:

y = f(x)

and

y' = f(x - A)

in y, when x = 0 we have f(0).

While to have this same point in y', we need to evaluate in x = A.

f(A - A) = f(0).

Then the value f(0) is now at x = A, this means that the point moved A units to the right.

And you can do this for all the values, so you will find that the entire graph of f(x) has ben moved A units to the right.

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3 years ago

What is the vertex of the graph of the function below? <br><br>y = x2 + 8x + 12

Vera_Pavlovna [14]

Hello,

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