The slope point form is
m is the slope
x1, y1 are the coordinates of a point on the line
The slope of the line is -1
m = -1
point (-5, -4) lies on the line
x1 = -5 and y1 = -4
Let us substitute them in the form above
Remember (-)(-) = (+)
The equation of the line in the slope-point form is y + 4 = -1(x + 5)
Answer:
m = - 2 is the value of m that the function y= e^mx is a solution of the differential equation, y' + 2y = 0.
Step-by-step explanation:
To determine all values of m so that the function y= e^mx is a solution of the given differential equation.
First, we will find y'.
From, y= e^mx
But,
Hence,
∴
Now, we will put the values of y' and y into the given differential equation y' + 2y =0
From the question,
and
Then, becomes
Then,
∴
Hence, m = - 2 is the value of m that the function y= e^mx is a solution of the differential equation, y' + 2y = 0.