Solve the differential equations.
dy = 4 − x
/
dx
We have dy/dx = (4-x) dx which is a first order linear ODE
dy = (4-x) dx. Now integrating both sides we get:
y = 4x - 1/2 x^2 + C
which is the answer. Note we only wrote +c once since we can combine arbitrary constants under addition and subtraction with each other.
Answer:
$12.92
Step-by-step explanation:
The linear equation representing the line passing through the points (0, 4) and (2, -2) is y=−3x+4.
Here, we have to write a linear equation that represents the line passing through the points (0, 4) and (2, -2), we can use the point-slope form of a linear equation:
where:
m is the slope of the line,
is one of the given points on the line.
Given the points (0, 4) and (2, -2),
let's calculate the slope m:
m= −2−4/ 2−0
= −6/2
=−3.
Now, use the point-slope form with the point (0, 4):
y−4=−3(x−0).
Simplify the equation:
y−4=−3x.
Add 4 to both sides:
y=−3x+4.
So, the linear equation representing the line passing through the points (0, 4) and (2, -2) is y=−3x+4.
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Answer:
y=-3x+4
Step-by-step explanation:
it's negative bc the slope is going from left to right. you just have to do rise over run to find the slope.