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3 years ago

Find equation of the line that contains the point (4,-2) and is perpendicular to the line y= _2x+8

Mathematics

2 answers:

madreJ [45]3 years ago

6 0

9514 1404 393

Answer:

y = 1/2x -4

Step-by-step explanation:

We presume the given line is ...

y = -2x +8

This is in slope-intercept form, which allows us to determine easily that the slope of this line is -2.

A perpendicular line will have a slope that is the opposite reciprocal of -2:

m = -1/(-2) = 1/2

The y-intercept of the desired line can be found from the point (x, y) = (4, -2) using the equation ...

b = y - mx

b = -2 -(1/2)(4) = -4

Now, we know the slope and y-intercept of the desired perpendicular line through (4, -2), so we can write its equation as ...

y = 1/2x -4

Additional comment

"Slope-intercept form" is ...

y = mx + b . . . . . . where m is the slope and b is the y-intercept

xz_007 [3.2K]3 years ago

3 0

Answer:

y = 1/2x - 4

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = -2x + 8. Its slope is -2. A line perpendicular to this one will have a slope of 1/2.

Plug this value (1/2) into your standard point-slope equation of y = mx + b.

y = 1/2x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (4, -2). Plug in the x and y values into the x and y of the standard equation.

-2 = 1/2(4) + b

To find b, multiply the slope and the input of x (4)

-2 = 2 + b

Now, subtract 2 from both sides to isolate b.

-4 = b

Plug this into your standard equation.

y = 1/2x - 4

This equation is perpendicular to your given equation (y = -2x + 8) and contains point (4, -2)

Hope this helps!

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timurjin [86]

Answer:

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Step-by-step explanation:

5(x-5)=3(x-7)

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Add 25 to each side

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3 years ago

A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 166 feet and a maximum height of 40 feet. Find

scoray [572]

Answer:

38.27775 feet

Step-by-step explanation:

The bridge has been shown in the figure.

Let the highest point of the parabolic bridge (i.e. vertex of the parabola) be at the origin, $O(0,0)$ in the cartesian coordinate system.

As the bridge have the shape of an inverted parabola, so the standard equation, which describes the shape of the bridge is

$x^2=4ay\;\cdots(i)$

where $a$ is an arbitrary constant (distance between focus and vertex of the parabola).

The span of the bridge = 166 feet and

Maximum height of the bridge= 40 feet.

The coordinate where the bridge meets the base is $A(83, -40)$ and $B(-83, -40).$

There is only one constant in the equation of the parabola, so, use either of one point to find the value of $a$ .

Putting $A(83,-40)$ in the equation (i) we have

$83^2=4a(-40)$

$\Rightarrow a=-43.05625$

So, on putting the value of $a$ in the equation (i), the equation of bridge is

$x^2=-172.225y$

From the figure, the distance from the center is measured along the x-axis, x coordinate at the distance of 10 feet is, $x=\pm 10$ feet, put this value in equation (i) to get the value of y.