Hello there! So, y = mx + b is in slope-intercept form, where m represents the slope, b represents the y-intercept, and y and x remain unfilled. First off, let's solve for the slope. The formula for slope is y2 - y1 / x2 - x1, where you subtract the first x and y coordinates from the second x and y coordinates. So it would be formed like this:

9 - 4 / 6 - (-4)

Let's subtract. 9 - 4 is 5. 6 - (-4) is 10. 5/10 is 1/2 in simplest form. The slope for this equation is 1/2. Now, let's find the y-intercept. We will find that by plugging one of the points into the equation and solving for b. The x and y coordinates will be filled in by that coordinate. Let's use (-4, 4) for this problem. We will also plug in the slope. In this case, the problem will look like this:

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

Now, let's multiply 1/2 and -4 to get -2. Now, to get b by itself, subtract 2 to both sides to isolate the b. -2 + 2 cancels out. 4 + 2 is 6. b = 6. There. The equation of the line in slope-intercept form is y = 1/2x + 6.

6 0

4 years ago

A rocket is fired upward with an initial velocity v of 80 meters per second. The quadratic function S(t)=−5t2+80t can be used to

grin007 [14]

9514 1404 393

Answer:

a) 320 m

b) 4.838 seconds, or 11.162 seconds

Step-by-step explanation:

a) S(8) = -5(8^2) +80(8) = -320 +640 = 320

The height 8 seconds after takeoff will be 320 meters.

b) S(t) = 270

270 = -5t^2 +80t

-54 = t^2 -16t . . . . . . divide by -5

10 = t^2 -16t +64 . . . . add 64

±√10 = t -8 . . . . . . . . . . take the square root

t = 8 ±√10 ≈ {4.838, 11.162}

The rocket will be at a height of 270 meters at 4.838 and 11.162 seconds after takeoff.

4 0

3 years ago