All categories

2 years ago

How do I find slope intercept for a line that passes through (4,-4) with a slope of -1

Mathematics

2 answers:

yarga [219]2 years ago

3 0

Answer:

y = -x

Step-by-step explanation:

Use the equation:

y = mx + b

where m is the slope and b is the y-intercept.

In this case, there is no y intercept, as we can see by manipulating the point-slope equation:

y + 4 = -1(x + 4)

y = -x + 0

So, the equation for this line is y = -x.

skad [1K]2 years ago

3 0

Y=-1x
or
y=-1x + 0

Considering you already have the slope & a point you end up having

Y = mx + b

-4 which is your Y so

-4=mx + b

M is your slope so

-4=-1(x) + b

Your x is 4 so

-4= -1(4) + b

B is your y intercept but because -4 = -1 times 4 your b is zero

You might be interested in

On Monday, 30% of the 900 students at Maple Middle school walk to school. Complete the double numberline model. How many student

vagabundo [1.1K]

the answer is 270 (dont click ant links in this app)

8 0

3 years ago

if there are two containers of sugar solution, the first is 4% concentration and second is 8% concentration. how much of each sh

Elina [12.6K]

Answer:

<u>30 gallons solution 4% and 10 gallons solution 8%</u>

Step-by-step explanation:

x=40-y

4(40-y)+8y=200

160-4y+8y=200

4y=200-160

4y=40 => y=10 (gallons solution 8%)

=> x=40-10=30 (gallons solution 4%)

30 gallons solution 4% and 10 gallons solution 8%

5 0

3 years ago

Farmer Bob is trying to figure out how much space he has for his garden. If the sides of the garden are 10 ft and 50 ft, what is

Svetach [21]

The area of the garden 10 ft•50 ft= 500 sq ft

5 0

4 years ago

what is the realtionship between the value of the digital 4 in the numbers 5,412 and the number 54,123?

REY [17]

Times 10 400 times ten is 4000

6 0

3 years ago

Read 2 more answers

In the triangle pictured, let A, B, C be the angles at the three vertices, and let a,b,c be the sides opposite those angles. Acc

Troyanec [42]

Answer:

Step-by-step explanation:

(a)

Consider the following:

$A=\frac{\pi}{4}=45°\\\\B=\frac{\pi}{3}=60°$

Use sine rule,

$\frac{b}{a}=\frac{\sinB}{\sin A}
\\\\=\frac{\sin{\frac{\pi}{3}}
}{\sin{\frac{\pi}{4}}}\\\\=\frac{[\frac{\sqrt{3}}{2}]}{\frac{1}{\sqrt{2}}}\\\\=\frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{1}=\sqrt{\frac{3}{2}}$

Again consider,

$\frac{b}{a}=\frac{\sin{B}}{\sin{A}}
\\\\\sin{B}=\frac{b}{a}\times \sin{A}\\\\\sin{B}=\sqrt{\frac{3}{2}}\sin {A}\\\\B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

Thus, the angle B is function of A is, $B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

Now find $\frac{dB}{dA}$

Differentiate implicitly the function $\sin{B}=\sqrt{\frac{3}{2}}\sin{A}$ with respect to A to get,

$\cos {B}.\frac{dB}{dA}=\sqrt{\frac{3}{2}}\cos A\\\\\frac{dB}{dA}=\sqrt{\frac{3}{2}}.\frac{\cos A}{\cos B}$

When $A=\frac{\pi}{4},B=\frac{\pi}{3}$ , the value of $\frac{dB}{dA}$ is,

$\frac{dB}{dA}=\sqrt{\frac{3}{2}}.\frac{\cos {\frac{\pi}{4}}}{\cos {\frac{\pi}{3}}}\\\\=\sqrt{\frac{3}{2}}.\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}\\\\=\sqrt{3}$

In general, the linear approximation at x= a is,

$f(x)=f'(x).(x-a)+f(a)$

Here the function $f(A)=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

At $A=\frac{\pi}{4}$

$f(\frac{\pi}{4})=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{\frac{\pi}{4}}]\\\\=\sin^{-1}[\sqrt{\frac{3}{2}}.\frac{1}{\sqrt{2}}]\\\\\=\sin^{-1}(\frac{\sqrt{2}}{2})\\\\=\frac{\pi}{3}$

And,

$f'(A)=\frac{dB}{dA}=\sqrt{3}$ from part b

Therefore, the linear approximation at $A=\frac{\pi}{4}$ is,

$f(x)=f'(A).(x-A)+f(A)\\\\=f'(\frac{\pi}{4}).(x-\frac{\pi}{4})+f(\frac{\pi}{4})\\\\=\sqrt{3}.[x-\frac{\pi}{4}]+\frac{\pi}{3}$

Use part (c), when $A=46°$ , B is approximately,

$B=f(46°)=\sqrt{3}[46°-\frac{\pi}{4}]+\frac{\pi}{3}\\\\=\sqrt{3}(1°)+\frac{\pi}{3}\\\\=61.732°$

8 0

3 years ago