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PIT_PIT [208]
2 years ago
13

find an equation for the line that passes through (-4, 8) and (3, -7). what is the slope? where does the line intersect the x-ax

is and the y-axis?
Mathematics
1 answer:
leonid [27]2 years ago
7 0
(x_1;\ y_1);\ (x_2;\ y_2)\\\\the\ slope:m=\dfrac{y_2-y_1}{x_2-x_1}\\\\the\ slope\ form\ of\ the\ line:y=mx+b\\the\ point-slope\ form:y-y_1=m(x-x_1)\\-------------------\\\\(-4;\ 8)\to x_1=-4;\ y_1=8\\(3;-7)\to x_2=3;\ y_2=-7\\\\m=\dfrac{-7-8}{3-(-4)}=\dfrac{-15}{3+4}=-\dfrac{15}{7}\\\\\\y-8=-\dfrac{15}{7}(x-(-4))\\\\y-8=-\dfrac{15}{7}x-\dfrac{60}{7}\\\\y=-\dfrac{15}{7}x-\dfrac{4}{7}\\\\x-intercept\ when\ y=0\\-\dfrac{15}{7}x-\dfrac{4}{7}=0\ \ \ |\cdot7\\\\-15x-4=0\ \ \ |+4\\\\-15x=4\ \ \ |:(-15)

x=-\dfrac{4}{15}\to\left(-\dfrac{4}{15};\ 0\right)\\\\y-intrcept\ when\ x=0\\\\y=-\dfrac{15}{7}\cdot0-\dfrac{4}{7}\\\\y=-\dfrac{4}{7}\to\left(0;-\dfrac{4}{7}\right)
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6 0
3 years ago
I don’t really get this one.<br> Thx and have a great day!!
gayaneshka [121]

Answer:

The correct option is C). (9,4)

The coordinates of a point N is (9,4)

Step-by-step explanation:

Theory: If point P(x,y) lies on line segment AB and AP: PB=m:n, then we say P divides line AB internally in ratio of m:n and Point is given by

P=(\frac{mX2+nX1}{m+n} , \frac{mY2+nY1}{m+n})

Given that point, M is lying somewhere between point L and point N.

The coordinates of a point L is (-6,14)

The coordinates of a point M is (-3,12)

Also, LM: MN = 1:4

We can write as,

Let,

Point L(-6,14)=(X1, Y1)

Point M(-3,12)=(x,y)

Point N is (X2, Y2)

m=1 and n=4

M(-3,12)=(\frac{mX2+nX1}{m+n} , \frac{mY2+nY1}{m+n})

M(-3,12)=(\frac{1(X2)+4(-6)}{1+4} , \frac{(Y2)+4(14)}{1+4})

M(-3,12)=(\frac{(X2)-24}{5} , \frac{1(Y2)+56}{5})

(-3)=\frac{(X2)-24}{5}

(-15)=X2-24

X2=9

(12)=\frac{(Y2)+56}{5}

(60)=Y2+56

Y2=4

Thus,

The coordinates of a point N is (9,4)

Result: The correct option is C). (9,4)

3 0
3 years ago
Cqn someone answer this?​
Norma-Jean [14]

Answer:

  • -3

Step-by-step explanation:

  • -11/2+27/4+(-17/4)
  • (-22+27-17)/4
  • (-12)/4
  • -3

7 0
3 years ago
Read 2 more answers
Can someone please help? A ferris wheel is drawn on a coordinate plane so that the first car is located at the point ​(0​,10​).
Ugo [173]

Answer:

(10,0)

Step-by-step explanation:

When it comes to rotations by 90 degrees or 270 degrees, you just have to switch the order of x- and y- coordinates. Then find the sign by considering which quadrant will it be. In this case, it is originally on the positive y-axis and now it would be +ve x-axis.

5 0
3 years ago
H 24 inches The volume of a cylinder can be found by using the formula v Bh. Which expression can be used to determine B, the ar
Lelechka [254]
The volume a cylinder is v=(area of base)h and since the area of the base is πr², you can write the equation a v=πr²h.  Since the problem wants us to find what be is in the equation of a cylinder as v=Bh, we know that B=πr².  The problem gave us the diameter of the circle so we no the radius is going to be the diameter (24) divided by 2 which equals 12.  therefore B=12²π.

I hope this helps. 
6 0
2 years ago
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