Which is the equation of a line that has a slope of 4 and passes through point (1, 6)?

Mathematics

2 answers:

tankabanditka [31]2 years ago

6 0

The answer would be Y=4x+6

Veronika [31]2 years ago

3 0

Y=4x+6 would be the answer

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Solve the following system of equations. Show all work and solutions.

Hitman42 [59]

y=2x²+6x+1
y=-4x²+1

Make the equations equal and solve for x

2x²+6x+1=-4x²+1
6x²+6x=0
6x(x+1)=0
6x=0 or x+1=0
x=0 or x=-1

For x=0

y=-4(0)+1=1

For x=-1

y=-4(1)+1=-3

The solutions are

(0,1) and (-1,-3)

Graph attached

4 0

1 year 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: