How do you find the missing outputs to a function when the slope is given along with a solution ?

The easiest way to find a missing output when you have a slope and a solution is to solve for the equation and then use the input.

For instance, if you were given a slope (m) of 3 and a solution of (2, 7). Then you would use all of that information in slope intercept form to find the intercept.

y = mx + b

Insert slope (m) and the point.

7 = 3(2) + b

Now multiply and solve for b.

7 = 6 + b

1 = b

Now that we have the value of b, we can write the equation using that and the slope as y = 3x + 1. Now no matter what the input (x) is, we can find the output (y).

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west