Write the equation of the line that passes through (3, -2) and has a slope of 4 in point slope form

Mathematics

2 answers:

Angelina_Jolie [31]3 years ago

6 0

y = mx + b is the equation of a line;

m = slope , b = y-intercept

m = 4 : so we have : y = 4 x +b

We are give a set of points which it passes through, we can simply plug them in:

-2 = 4(3) + b (3 is the x and -2 is the y)

Then: -2 = 12 +b -14 = b

The final equation is : y = 4 x - 14

The answer is: y = 4 x - 14

I hope this helps have a fantastic day!!

diamong [38]3 years ago

4 0

y=mx+b is the equation of a line;

m=slope , b= y-intercept

m=4 ; so we have : y=4x+b

We are give a set of points which it passes through, we can simply plug them in:

-2 = 4(3)+b (3 is the x and -2 is the y)

We get -2 = 12 +b .... -14=b

our final equation is : y=4x-14

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F(x)=-1/2(x-2)^2-4 <br> Graph the function

telo118 [61]

Answer:

see below

Step-by-step explanation:

The function is written in vertex form. It has a negative vertical scale factor, so you know ...

the vertex is (2, -4)
the vertical scale factor is 1/2
the parabola opens downward

Vertex form is ...

f(x) = a(x -h)^2 +k . . . . . . . . . . vertical scale factor "a", vertex (h, k)

Since you know the vertex and scale factor, you can plot some points on the graph. I find it convenient to think in terms of units either side of the vertex. These are values of x that would make (x-2)^2 be 1^2, 2^2, 3^2, 4^2 and so on. The vertical scale factor of -1/2 tells you that the y-differences for these points will be -1/2, -4/2, -9/2, -16/2 from the vertex. Then we have ...

vertex: (2, -4)

1 unit either side of the vertex: (1, -4.5), (3, -4.5)

2 units either side of the vertex: (0, -6), (4, -6)

3 units either side of the vertex: (-1, -8.5), (5, -8.5)

4 units either side of the vertex: (-2, -12), (6, -12)

You can plot these points and draw a smooth curve through them. Or, you can let a graphing calculator do it. The result will be similar to that shown below.